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Chenglong Yu

Publications and source records attributed to Chenglong Yu.

At least 19 recordsLinked to original sources
arXiv2026

Commensurability Relations Between Deligne-Mostow-Thurston and Ghazouani-Pirio Monodromy Groups

We classify commensurability relations between Deligne--Mostow--Thurston monodromy groups and the sixteen arithmetic Ghazouani--Pirio monodromy groups arising from moduli of flat cone metrics on the sphere and on the torus. In both settings, the monodromy group preserves a skew-Hermitian form coming from twisted homology. We use a degeneration method to compute their determinant classes in the genus one case. The defining CM fields and determinant classes of the skew-Hermitian forms determine the commensurability relations. In particular, each of the sixteen arithmetic Ghazouani--Pirio monodromy groups is commensurable with an arithmetic Deligne--Mostow--Thurston monodromy group.

math.GT↗
arXiv2026

Monodromy Eigenvalues of Milnor Fibers for Line Arrangements

It is an important problem to know whether the monodromy on the cohomology of Milnor fibers associated to hyperplane arrangements is a combinatorial invariant. In this paper, we obtain a combinatorial vanishing criterion for certain eigenspaces of this algebraic monodromy in line arrangements. Combining with Hirzebruch inequality, which is a consequence of Bogomolov--Miyaoka--Yau inequality, we prove that for essential complex line arrangements, the eigenvalues of the monodromy have orders at most five. This is a partial progress toward Papadima--Suciu conjecture and proves Salvetti--Serventi connectivity conjecture. For essential complexified real line arrangements, the monodromy order is improved to at most four thanks to Shnurnikov's inequality. This confirms Papadima--Suciu conjecture for real line arrangements and also Yoshinaga's sharp pair conjecture.

math.AG↗
arXiv2026

ADGNet: Asymmetric Dual-text Guided Network for Infrared Small Target Detection

InfRared Small Target Detection (IRSTD) is a challenging task. Relying solely on pixel-level information, vision-only methods struggle to distinguish targets from clutter. Current multimodal methods typically describe both targets and backgrounds with a single textual prompt. Such an approach lacks dedicated regional guidance and ignores infrared semantic asymmetry. Consequently, it provides insufficient background suppression information and introduces severe feature optimization conflicts, overwhelming small targets with noise. To address these issues, we propose a novel Asymmetric Dual-text Guided Network (ADGNet). Specifically, accounting for the infrared semantic asymmetry, we first design the Asymmetric Dual-text Prompt (ADP), comprising an image-agnostic abstract target prompt and an image-specific detailed background prompt. To leverage these prompts, we introduce an Asymmetric Dual-Branch Interaction (ADBI) module to separately guide visual features with their respective text priors, protecting targets from noise while suppressing background clutter. Subsequently, we introduce an Adaptive Feature Aggregation (AFA) module to dynamically fuse features from the two branches. Furthermore, we construct a multimodal Asymmetric Image-Text Infrared (AITIR) dataset by providing asymmetric text annotations for three public datasets (IRSTD-1K, NUDT-SIRST, and SIRST). Extensive experiments demonstrate that ADGNet outperforms 21 state-of-the-art (SOTA) methods. Code is available at https://github.com/iLearn-Lab/MM26-ADGNet.

cs.CV↗
arXiv2026

DGNet: Dual-knowledge Guided Network for Infrared Small Target Detection

InfRared Small Target Detection (IRSTD) is a prominent and challenging task in computer vision. In recent years, text-guided methods have significantly improved detection performance. However, they still suffer from two key limitations. First, a single text description simultaneously modeling both background and target leads to semantic entanglement, which contradicts the objective of background suppression and target enhancement. Second, reliance on image-specific textual prompts (requiring additional external models such as CLIP during inference) results in deployment constraints. To address these issues, we propose a novel Dual-knowledge Guided Network (DGNet) based on multiple generalizable texts. Specifically, we design a Prior-knowledge Wavelet Modulation (PWM) module, which leverages dual textual priors that separately characterize large-scale backgrounds and sparse targets to effectively disentangle and modulate entangled semantics in the frequency domain. Furthermore, we introduce a Consensus-knowledge Directional Alignment (CDA) loss, which models the initial state and the ideal target across samples as `complex background' and `bright target', respectively, thereby constructing a clear and unified directional optimization trajectory for the model. Extensive experiments on three public datasets demonstrate the superior performance of DGNet and the effectiveness of each component. The source code is available at https://github.com/iLearn-Lab/MM26-DGNet.

cs.CV↗
arXiv2026

Log-concavity from enumerative geometry of planar curve singularities

We propose a log-concavity conjecture for BPS invariants arising in the enumerative geometry of planar curve singularities, identified with the local Euler obstructions of Severi strata in their versal deformations. We further extend this conjecture to ruling polynomials of Legendrian links and to E-polynomials of character varieties. We establish these conjectures for irreducible weighted-homogeneous singularities (torus knots) and for ADE singularities, and prove a multiplicative property for ruling polynomials compatible with log-concavity.

math.AG↗
arXiv2026

Double integrals and transformation formulas for Appell--Lauricella hypergeometric functions $F_D$

The monodromy of hypergeometric functions can govern the properties of the functions themselves. Previously, the second and third authors studied the commensurability relations among monodromy groups of the Appell--Lauricella hypergeometric functions using Deligne--Mostow theory and the geometric correspondence between curves and surfaces. In this paper, we apply the same construction to obtain transformation formulas among these hypergeometric functions. This also provides an alternative approach to some of Goursat's quadratic transformations via double integrals and Fubini's theorem.

math.CA↗
arXiv2026

Rigidity Criterion for Certain Calabi-Yau Families

We prove a new rigidity criterion for families of polarized Calabi--Yau manifolds. Motivated by known non-rigid examples, we conjecture that a family over a quasi-projective curve is rigid if, near a boundary point, the total space is smooth, the relative canonical bundle is trivial, and the boundary fiber contains an isolated singular point. We verify this conjecture when one such isolated singularity has a concentrated mixed Hodge spectrum, a class including ordinary double points and cusps. The proof combines a local vanishing-cycle analysis with a global tensor-product decomposition of the associated variation of Hodge structures.

math.AG↗
arXiv2025

Homology of Local Systems on Real Line Arrangement Complements

We study the homology groups of the complement of a complexified real line arrangement with coefficients in complex rank-one local systems. Using Borel--Moore homology, we establish an algorithm computing their dimensions via the real figures of the arrangement. It enables us to give a new upper bound. We further consider the case where the arrangement contains a sharp pair and make partial progress on a conjecture proposed by Yoshinaga.

math.AG↗
arXiv2025

Moduli spaces of sextic curves with simple singularities and their compactifications

In this paper, we study moduli spaces of sextic curves with simple singularities. Through period maps of K3 surfaces with ADE singularities, we prove that such moduli spaces admit algebraic open embeddings into arithmetic quotients of type IV domains. For all cases, we prove the identifications of GIT compactifications and Looijenga compactifications. We also describe Picard lattices in an explicit way for many cases. For nodal cases, we prove that the orbifold structures on the two sides of the period map are isomorphic.

math.AG↗
arXiv2025

The{N/D}-Conjecture for Nonresonant Hyperplane Arrangements

This paper studies Bernstein--Sato polynomials $b_{f,0}$ for homogeneous polynomials $f$ of degree $d$ with $n$ variables. It is open to know when $-{n\over d}$ is a root of $b_{f,0}$. For essential indecomposable hyperplane arrangements, this is a conjecture by Budur, Musta\c{t}\u{a} and Teitler and implies the strong topological monodromy conjecture for arrangements. Walther gave a sufficient condition that a certain differential form does not vanish in the top cohomology group of Milnor fiber. We use Walther's result to verify the $n\over d$-conjecture for weighted hyperplane arrangements satisfying the nonresonant condition.

math.AG↗
arXiv2024

Commensurability Among Deligne-Mostow Monodromy Groups

This paper gives the commensurability classification of Deligne--Mostow ball quotients and shows that the 104 Deligne--Mostow lattices form 38 commensurability classes. First, we find commensurability relations among Deligne--Mostow monodromy groups, which are not necessarily discrete. This generalizes previous work by Sauter and Deligne--Mostow in dimension two. In this part, we consider certain projective surfaces with two fibrations over the projective line, which induce two sets of Deligne--Mostow data. Correspondences between moduli spaces provide a geometric realization of commensurability relations. Secondly, we obtain commensurability invariants from conformal classes of Hermitian forms and toroidal boundary divisors. This completes the commensurability classification of Deligne--Mostow lattices and provides an alternative approach to the results of Kappes--M{\"o}ller and McMullen on non-arithmetic Deligne--Mostow lattices.

math.AG↗
arXiv2024

Deformations of highly symmetric Calabi-Yau Grassmannian hypersurfaces

We use arithmetic and Hodge-theoretic techniques to study pencils of Calabi-Yau varieties realized as highly symmetric hypersurfaces in Grassmannians and their quotients, demonstrating that their geometric properties are distinct from the classical mirrors of Calabi-Yau Grassmannian hypersurfaces.

math.AG↗
arXiv2024

Calabi-Yau Varieties via Cyclic Covers, and Complex Hyperbolic Structures for their Moduli Spaces

In this paper we mainly study Calabi--Yau varieties that arise as triple covers of products of projective lines branched along simple normal crossing divisors. For some of those families of Calabi--Yau varieties, the period maps factor through arithmetic quotients of complex hyperbolic balls. We give a classification of such examples. One of the families was previously studied by Voisin, Borcea and Rohde. For these ball-type cases, we will show arithmeticity of the monodromy groups. These ball quotients are all commensurable to ball quotients in Deligne--Mostow theory. As a byproduct, we prove some commensurability relations among arithmetic groups in Deligne--Mostow theory.

math.AG↗
arXiv2018

Moduli of Nodal Sextic Curves via Periods of K3 Surfaces

In this paper we study the moduli spaces of nodal sextic curves. We realize each irreducible component of the GIT space of sextic curves with given number of nodes as an open subspace of type IV arithmetic quotients. We then focus on the compactifications of the moduli spaces, one side is the geometric (GIT) compactifications, the other side is the Hodge theoretic compactifications such as Looijenga compactifications and Baily--Borel compactifications. The main result is the isomorphism between GIT and Looijenga compactifications. Some examples are closely related to del Pezzo surfaces. We also extend our results to moduli of nodal sextic curves with specified symmetry.

math.AG↗
arXiv2018

Moduli Spaces of Symmetric Cubic Fourfolds and Locally Symmetric Varieties

In this paper we realize the moduli spaces of cubic fourfolds with specified automorphism groups as arithmetic quotients of complex hyperbolic balls or type IV symmetric domains, and study their compactifications. Our results mainly depend on the well-known works about moduli space of cubic fourfolds, including the global Torelli theorem proved by Voisin ([Voi86]) and the characterization of the image of the period map, which is given by Laza ([Laz09, Laz10]) and Looijenga ([Loo09]) independently. The key input for our study of compactifications is the functoriality of Looijenga compactifications, which we formulate in the appendix (section A). The appendix can also be applied to study the moduli spaces of singular K3 surfaces and cubic fourfolds, which will appear in a subsequent paper.

math.AG↗
arXiv2018

Jacobian rings for homogenous vector bundles and applications

In this note, we examine the Jacobian ring description of the Hodge structure of zero loci of vector bundle sections on a class of ambient varieties. We consider a set of cohomological vanishing conditions that imply such a description, and we verify these conditions for some new cases. We also observe that the method can be directly extended to log homogeneous varieties. We apply the Jacobian ring to study the null varieties of period integrals and their derivatives, generalizing a result in [9] for projective spaces. As an additional application, we prove the Hodge conjecture for very generic hypersurfaces in certain generalized flag varieties.

math.AG↗
arXiv2018

Hasse-Witt matrices, unit roots and period integrals

Motivated by the work of Candelas, de la Ossa and Rodriguez-Villegas [6], we study the relations between Hasse-Witt matrices and period integrals of Calabi-Yau hypersurfaces in both toric varieties and partial flag varieties. We prove a conjecture by Vlasenko [23] on higher Hasse-Witt matrices for toric hypersurfaces following Katz's method of local expansion [14, 15]. The higher Hasse-Witt matrices also have close relation with period integrals. The proof gives a way to pass from Katz's congruence relations in terms of expansion coefficients [15] to Dwork's congruence relations [8] about periods.

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