arXiv subjects

Ya Deng

Publications and source records attributed to Ya Deng.

At least 19 recordsLinked to original sources

arXiv2026

A flatness criterion for pseudo-effective sheaves on compact K\"ahler spaces

In this paper, we prove that if $E$ is a pseudo-effective sheaf with vanishing first Chern class on a klt compact K\"ahler space $X$, then, after passing to a finite quasi-\'etale cover, the reflexive pullback of $E$ is locally free and flat. This extends the flatness criterion of H\"oring--Peternell, originally established for projective varieties, to the K\"ahler setting. The proof relies on two main ingredients, both of which are new even in the projective case. The first is a flatness theorem for stable sheaves: we show that a slope-stable pseudo-effective sheaf with vanishing first Chern class is Hermitian flat. This is obtained by combining Hermitian--Einstein theory with the subharmonicity properties of direct image sheaves. The second is a singular K\"ahler analogue of Simpson's flatness theorem for extensions of locally free Hermitian flat sheaves.

math.AG↗

arXiv2026

Controlled chemical vapor deposition for synthesis of emerging Mo(W)Te2 systems

The Group-VI transition metal ditellurides offer a rich platform for correlated and topological phenomena, yet their structural polymorphism and instability complicate the creation of single crystals and heterointerfaces. Here, we introduce a confined-space chemical vapor deposition (CVD) strategy that lowers the growth temperature window and, when combined with tailored precursor configurations and stepwise thermal ramps, enables the deterministic synthesis of high-quality single crystals, alloys, and lateral/vertical heterostructures. High-resolution aberration-corrected STEM provides atomic characterization of lattice-matched Mo(W)Te2 lateral heterostructure, revealing nearly atomically sharp, compositionally well-defined seamless boundaries. This approach avoids the thickness nonuniformity and structural limitations commonly associated with exfoliated samples, enabling reproducible fabrication of clean heterointerfaces and establishing a nearly ideal in-situ experimental system. Furthermore, scanning tunneling microscopy and spectroscopy (STM and STS) enable direct imaging of the seamless boundaries in Mo(W)Te2 lateral heterostructures, while uncovering their distinct real-space distributions of the local density of states. Our results establish a scalable pathway for engineering crystalline Te-based structures with controlled geometry and stacking, providing an essential step toward quantum and topological device platforms based on the transition metal ditellurides family.

cond-mat.mtrl-sci↗

arXiv2026

Two-step nilpotent monodromy of local systems on special varieties

Let $X$ be a smooth complex quasi-projective variety that is special in the sense of Campana. We prove that the monodromy group of any complex local system on $X$ is virtually nilpotent of class at most $2$. This result sharply refines a theorem of Cadorel, Yamanoi, and the second author. To establish this result, we develop a deformation theory for certain local systems on quasi-compact K\"ahler manifolds by constructing universal deformations for such local systems. As a byproduct of our argument, we also show that a general fiber of the quasi-Albanese map of $X$ is special, extending a result of Campana and Claudon from the projective to the quasi-projective setting.

math.AG↗

arXiv2025

Topology, Hyperbolicity, and the Shafarevich Conjecture for Complex Algebraic Varieties

This survey presents recent developments concerning the Shafarevich conjecture, non-abelian Hodge theories, hyperbolicity, and the topology of complex algebraic varieties, as well as the interplay among these areas. More precisely, we present the main ideas and techniques involved in the linear versions of the following conjectures: the Shafarevich conjecture, the Chern-Hopf-Thurston conjecture, Koll\'ar's conjecture on the holomorphic Euler characteristic, the de Oliveira-Katzarkov-Ramachandran conjecture, and Campana's nilpotency conjecture. In addition, we discuss characterizations of the hyperbolicity of complex quasi-projective varieties via representations of their fundamental groups, together with the generalized Green-Griffiths-Lang conjecture in the presence of a big local system.

math.AG↗

arXiv2025

Hyperbolicity and fundamental groups of complex quasi-projective varieties (III): applications

This paper is Part III of a series of three. We begin by introducing the notion of $h$-special varieties, which can be seen as varieties "chain-connected by the Zariski closures of entire curves." We prove that if $X$ is either a special complex quasi-projective variety in the sense of Campana or an $h$-special variety, then for any linear representation $\varrho:\pi_1(X)\to \mathrm{GL}_N(\mathbb{C})$, the image $\varrho(\pi_1(X))$ is virtually nilpotent. We also provide examples showing that this result is sharp, leading to a revised form of Campana's abelianity conjecture for smooth quasi-projective varieties. In addition, we prove a structure theorem for quasi-projective varieties with big and semisimple representations of the fundamental groups, thereby addressing a conjecture by Koll\'ar in 1995. We also construct several examples of quasi-projective varieties that are special and $h$-special, highlighting certain atypical properties of the non-compact case in contrast with the projective setting.

math.AG↗

arXiv2025

Hyperbolicity and fundamental groups of complex quasi-projective varieties (II): via non-abelian Hodge theories

This is Part II of a series of three papers. We studies the hyperbolicity of complex quasi-projective varieties $X$ in the presence of a big and reductive representation $\varrho: \pi_1(X)\to {\rm GL}_N(\mathbb{C})$. For any Galois conjugate variety $X^\sigma$ with $\sigma \in {\rm Aut}(\mathbb{C}/\mathbb{Q})$, we prove the generalized Green-Griffiths-Lang conjecture. When $\varrho$ is furthermore large, we show that the special subsets of $X^\sigma$ describing the non-hyperbolicity locus coincide, and that this locus is proper exactly when $X$ is of log general type. Moreover, if the Zariski closure of $\rho(\pi_1(X))$ is semisimple, we prove that there exists a proper Zariski closed subset $Z \subsetneq X^\sigma$ such that every subvariety not contained in $Z$ is of log general type and all entire curves in $X^\sigma$ are contained in $Z$. This result extends the theorems of the third author (2010) and of Campana-Claudon-Eyssidieux (2015) from projective to quasi-projective varieties, and yields stronger conclusions even in the projective case.

math.AG↗

arXiv2025

Hodge theory for local systems and cohomological support loci

In this article, we pursue two main objectives. The first is to show that the fundamental results of Green-Lazarsfeld (1987, 1991) on generic vanishing theorems, and works of Budur-Wang (2015, 2020) on cohomology jumping loci, can be established within a unified framework based on suitable versions of the $\partial\bar{\partial}$-lemma. Our second-and primary-goal is to develop the technical tools required for this approach, namely an $L^2$-Hodge theory for the cohomology of rank-one local systems on quasi-compact K\"ahler manifolds. Further developments concerning higher-rank local systems, as well as several geometric applications, will be presented in a companion paper and are briefly outlined in the introduction.

math.AG↗

arXiv2025

Hyperbolicity and fundamental groups of complex quasi-projective varieties (I): Maximal quasi-Albanese dimension by Nevanlinna theory

This is the first part of a series of three papers. In this paper, we establish a Big Picard type theorem for holomorphic maps $f:Y \to X$, where $Y$ is a ramified covering of the punctured disc $\mathbb{D}^*$ with small ramification and $X$ is a complex quasi-projective variety of log-general type and of maximal quasi-Albanese dimension. As a byproduct, we prove the generalized Green-Griffiths-Lang conjecture for such $X$. This paper summarizes the parts of the three-paper series that are based primarily on Nevanlinna theory.

math.AG↗

arXiv2024

Deformation Openness of Big Fundamental Groups and Applications

In 2001, de Oliveira, Katzarkov, and Ramachandran conjectured that the property of smooth projective varieties having big fundamental groups is stable under small deformations. This conjecture was proven by Beno\^it Claudon in 2010 for surfaces and for threefolds under suitable assumptions. In this paper, we prove this conjecture for smooth projective varieties admitting a big complex local system. Moreover, we address a more general conjecture by Campana and Claudon concerning the deformation invariance of the $\Gamma$-dimension of projective varieties. As an application, we establish the deformation openness of pseudo-Brody hyperbolicity for projective varieties endowed with a big and semisimple complex local system. To achieve these results, we develop the deformation regularity of equivariant pluriharmonic maps into Euclidean buildings and Riemannian symmetric spaces in families, along with techniques from the reductive and linear Shafarevich conjectures.

math.AG↗

arXiv2024

Field-free superconducting diode effect and magnetochiral anisotropy in FeTe0.7Se0.3 junctions with the inherent asymmetric barrier

Nonreciprocal electrical transport, characterized by an asymmetric relationship between current and voltage, plays a crucial role in modern electronic industries. Recent studies have extended this phenomenon to superconductors, introducing the concept of the superconducting diode effect (SDE). The SDE is characterized by unequal critical supercurrents along opposite directions. Due to the requirement on broken inversion symmetry, the SDE is commonly accompanied by electrical magnetochiral anisotropy (eMCA) in the resistive state. Achieving a magnetic field-free SDE with field tunability is pivotal for advancements in superconductor devices. Conventionally, the field-free SDE has been achieved in Josephson junctions by intentionally intercalating an asymmetric barrier layer. Alternatively, internal magnetism was employed. Both approaches pose challenges in the selection of superconductors and fabrication processes, thereby impeding the development of SDE. Here, we present a field-free SDE in FeTe0.7Se0.3 (FTS) junction with eMCA, a phenomenon absent in FTS single nanosheets. The field-free property is associated with the presence of a gradient oxide layer on the upper surface of each FTS nanosheet, while the eMCA is linked to spin-splitting arising from the absence of inversion symmetry. Both the SDE and eMCA respond to magnetic fields with distinct temperature dependencies. This work presents a versatile and straightforward strategy for advancing superconducting electronics.

cond-mat.supr-con↗

arXiv2024

Existence and unicity of pluriharmonic maps to Euclidean buildings and applications

Given a complex smooth quasi-projective variety $X$, a reductive algebraic group $G$ defined over some non-archimedean local field $K$ and a Zariski dense representation $\varrho:\pi_1(X)\to G(K)$, we construct a $\varrho$-equivariant pluriharmonic map from the universal cover of $X$ into the Bruhat-Tits building $\Delta(G)$ of $G$, with appropriate asymptotic behavior. We also establish the uniqueness of such a pluriharmonic map in a suitable sense, and provide a geometric characterization of these equivariant maps. This paper builds upon and extends previous work by the authors jointly with G. Daskalopoulos and D. Brotbek.

math.CV↗

arXiv2024

$L^2$-vanishing theorem and a conjecture of Koll\'ar

In 1995, Koll\'ar conjectured that a smooth complex projective $n$-fold $X$ with generically large fundamental group has Euler characteristic $\chi(X, K_X)\geq 0$. In this paper, we prove the conjecture assuming $X$ has linear fundamental group, i.e., there exists a representation $\pi_1(X)\to {\rm GL}_N(\mathbb{C})$ with finite kernel. We deduce the conjecture by proving a stronger $L^2$ vanishing theorem: for the universal cover $\widetilde{X}$ of such $X$, its $L^2$-Dolbeault cohomology $H_{(2)}^{n,q}(\widetilde{X})=0$ for $q\neq 0$. The main ingredients of the proof are techniques from the linear Shafarevich conjecture along with some analytic methods.

math.AG↗

arXiv2024

Linear Chern-Hopf-Thurston conjecture

If $X$ is a closed $2n$-dimensional aspherical manifold, i.e., the universal cover of $X$ is contractible, then the Chern-Hopf-Thurston conjecture predicts that $(-1)^n\chi(X)\geq 0$. We prove this conjecture when $X$ is a complex projective manifold whose fundamental group admits an almost faithful linear representation over any field. In fact, we prove a much stronger statement that if $X$ is a complex projective manifold with large fundamental group and $\pi_1(X)$ admits an almost faithful linear representation, then $\chi(X, \mathcal{P})\geq 0$ for any perverse sheaf $\mathcal{P}$ on $X$. To prove this, we introduce a vanishing cycle functor of multivalued one-forms and apply techniques from non-abelian Hodge theory, both in archimedean and non-archimedean settings. These techniques allow us to deduce the desired positivity from the geometric properties of pure and mixed period maps.

math.AG↗

arXiv2024

Linear Shafarevich Conjecture in positive characteristic, Hyperbolicity and Applications

Given a complex quasi-projective normal variety $X$ and a linear representation $\varrho:\pi_1(X)\to {\rm GL}_{N}(K)$ with $K$ any field of positive characteristic, we mainly establish the following results: 1. the construction of the Shafarevich morphism ${\rm sh}_\varrho:X\to {\rm Sh}_\varrho(X)$ associated with $\varrho$. 2. In cases where $X$ is projective, $\varrho$ is faithful and the $\Gamma$-dimension of $X$ is at most two (e.g. $\dim X=2$), we prove that the Shafarevich conjecture holds for $X$. 3. In cases where $\varrho$ is big, we prove that the Green-Griffiths-Lang conjecture holds for $X$. 4. When $\varrho$ is big and the Zariski closure of $\varrho(\pi_1(X))$ is a semisimple algebraic group, we prove that $X$ is pseudo Picard hyperbolic, and strongly of log general type. 5. If $X$ is special or $h$-special, then $\varrho(\pi_1(X))$ is virtually abelian. We also prove Claudon-H\"oring-Koll\'ar's conjecture for complex projective manifolds with linear fundamental groups of any characteristic.

math.AG↗

arXiv2023

Quasi-finiteness of morphisms between character varieties

Let $f: Y\to X$ be a morphism between smooth complex quasi-projective varieties and $Z$ be the closure of $f(Y)$ with $\iota: Z\to X$ the inclusion map. We prove that a. for any field $K$, there exist finitely many semisimple representations $\{\tau_i:\pi_1(Z)\to {\rm GL}_N(\overline{k})\}_{i=1,\ldots,\ell}$ with $k\subset K$ the minimal field contained in $K$ such that if $\varrho:\pi_1(X)\to {\rm GL}_{N}(K)$ is any representation satisfying $[f^*\varrho]=1$, then $[\iota^*\varrho]=[\tau_i]$ for some $i$. b. The induced morphism between ${\rm GL}_{N}$-character varieties (of any characteristic) of $\pi_1(X)$ and $\pi_1(Y)$ is quasi-finite if ${\rm Im}[\pi_1(Z)\to \pi_1(X)]$ is a finite index subgroup of $\pi_1(X)$. These results extend the main results by Lasell in 1995 and Lasell-Ramachandran in 1996 from smooth complex projective varieties to quasi-projective cases with richer structures.

math.AG↗

arXiv2023

Reductive Shafarevich Conjecture

In this paper, we prove the holomorphic convexity of the covering of a complex projective {normal} variety $X$, which corresponds to the intersection of kernels of reductive representations $\rho:\pi_1(X)\to {\rm GL}_{N}(\mathbb{C})$, therefore answering a question by Eyssidieux, Katzarkov, Pantev, and Ramachandran in 2012. It is worth noting that Eyssidieux had previously proven this result in 2004 when $X$ is smooth. While our approach follows the general strategy employed in Eyssidieux's proof, it introduces several improvements and simplifications. Notably, it avoids the necessity of using the reduction mod $p$ method in Eyssidieux's original proof. Additionally, we construct the Shafarevich morphism for complex reductive representations of fundamental groups of complex quasi-projective varieties unconditionally, and proving its algebraic nature at the function field level.

math.AG↗

arXiv2022

Hyperbolicity and fundamental groups of complex quasi-projective varieties

This paper investigates the relationship between the hyperbolicity of complex quasi-projective varieties $X$ and the (topological) fundamental group $\pi_1(X)$ in the presence of a linear representation $\varrho: \pi_1(X) \to {\rm GL}_N(\mathbb{C})$. We present our main results in three parts. Firstly, we show that if $\varrho$ is bigand the Zariski closure of $\varrho(\pi_1(X))$ semisimple, then for any $X^\sigma:=X\times_\sigma\mathbb{C}$ where $\sigma\in {\rm Aut}(\mathbb{C}/\mathbb{Q})$, there exists a proper Zariski closed subset $Z \subsetneqq X^\sigma$ such that any closed irreducible subvariety $V$ of $X^\sigma$ not contained in $Z$ is of log general type, and any holomorphic map from the punctured disk $\mathbb{D}^*$ to $X^\sigma$ with image not contained in $Z$ does not have an essential singularity at the origin. In particular, all entire curves in $X^\sigma$ lie on $Z$. We provide examples to illustrate the optimality of this condition. Secondly, assuming that $\varrho$ is big and reductive, we prove the generalized Green-Griffiths-Lang conjecture for $X^\sigma$. Furthermore, if $\varrho$ is large, we show that the special subsets of $X^\sigma$ that capture the non-hyperbolicity locus of $X^\sigma$ from different perspectives are equal, and this subset is proper if and only if $X$ is of log general type. Lastly, we prove that if $X$ is a special quasi-projective manifold in the sense of Campana or $h$-special, then $\varrho(\pi_1(X))$ is virtually nilpotent. We provides examples to demonstrate that this result is sharp and thus revise Campana's abelianity conjecture for smooth quasi-projective varieties. To prove these theorems, we develop new features in non-abelian Hodge theory, geometric group theory, and Nevanlinna theory. Some byproducts are obtained.

math.AG↗

arXiv2022

Pluriharmonic maps into buildings and symmetric differentials

Given a complex smooth quasi-projective variety $X$, a semisimple algebraic group $G$ defined over some non-archimedean local field $K$ and a Zariski dense representation $\varrho:\pi_1(X)\to G(K)$, we construct a $\varrho$-equivariant (pluri-)harmonic map from the universal cover of $X$ into the Bruhat-Tits building $\Delta(G)$ of $G$, with some suitable asymptotic behavior. This theorem generalizes the previous work by Gromov-Schoen to the quasi-projective setting. As an application, we prove that $X$ has nonzero global logarithmic symmetric differentials if there exists a linear representation $\pi_1(X)\to {\rm GL}_N(\mathbb{K})$ with infinite image, where $ \mathbb{K}$ is any field. This theorem generalizes the previous work by Brunebarbe, Klingler and Totaro to the quasi-projective setting.

math.AG↗