arXiv subjects

Yen-An Chen

Publications and source records attributed to Yen-An Chen.

10 recordsLinked to original sources

arXiv2026

Boundedness of polarized foliated surfaces

We establish the minimal model program for klt adjoint foliated surfaces and use it to study the boundedness of polarized adjoint foliated surfaces. We prove that $ε$-lc adjoint foliated surfaces with nef adjoint canonical divisor and a nef and big integral polarization form a bounded family, provided that the volume of their sum is bounded from above. As applications, we establish boundedness and effective birationality for adjoint foliated surfaces of general type, as well as a uniform positive lower bound for their volumes. Finally, for $ε$-lc Calabi--Yau adjoint foliated surfaces, we prove that the volumes of the canonical divisors of rank one foliations on the underlying surfaces belong to a fixed discrete set.

math.AG↗

arXiv2026

On slope unstable Fano varieties

For Fano varieties, significant progress has been made recently in the study of $K$-stability, while the understanding of the weaker but more algebraic concept of $(-K)$-slope stability remains intricate. For instance, a conjecture attributed to Iskovskikh states that the tangent bundle of a Picard rank one Fano manifold is slope stable. Peternell-Wiśniewski and Hwang proved this conjecture up to dimension five in 1998, but Kanemitsu later disproved it in 2021. To address this gap in understanding, we present a method that aims to characterize the geometry associated with the maximal destabilizing sheaf of the tangent sheaf of a Fano variety. This approach utilizes modern advancements in the foliated minimal model program. In dimension two, our approach leads to a complete classification of $(-K)$-slope unstable weak del Pezzo surfaces with canonical singularities. As by-products, we provide the first conceptual proof that $\mathbb{P}^1 \times \mathbb{P}^1$ and $\mathbb{F}_1$ are the only $(-K)$-slope unstable nonsingular del Pezzo surfaces, recovering a classical result of Fahlaoui in 1989. We also uncover a phenomenon that does not occur for Fano manifolds: there exists a del Pezzo surface with type A singularities admitting a weak Kähler-Einstein metric, yet whose tangent sheaf is slope unstable.

math.AG↗

arXiv2026

On toric and toroidal foliations

In this paper, we provide toric descriptions for various foliation singularities on toric varieties, especially for non-dicritical singularities and F-dlt singularities. We then show that the toric foliated minimal model program works by demonstrating that non-dicritical singularities and F-dlt singularities are preserved.

math.AG↗

arXiv2025

ACC for foliated log canonical thresholds

It is known that the set of log canonical thresholds (lcts) on any varieties with fixed dimension satisfies the ascending chain condition. Inspired by the foliated minimal model program, it is intriguing to study the foliated version of lcts and ask whether they have the similar property. We give an affirmative answer in the case of surfaces and threefolds.

math.AG↗

arXiv2025

Boundedness of toric foliations

We discuss boundedness of toric Fano foliations and connectedness of its dicritical and singular loci. Moreover, we show the set of interpolated $δ$-lcts for the toric foliations satisfies the descending chain condition.

math.AG↗

arXiv2024

Existence of complements for foliations

This paper demonstrates the existence of $\mathbb{Q}$-complements for algebraically integrable log-Fano foliations on klt ambient varieties. Additionally, we investigate properties of algebraically integrable Fano foliations such as a partial inversion of adjunction as well as a connectedness principle.

math.AG↗

arXiv2022

Log canonical models of foliated surfaces

We study log canonical models of foliated surfaces of general type. In particular, we show that log canonical models of general type and their minimal partial du Val resolutions are bounded. Moreover, we show the valuative criteria of separatedness and properness and a property related to local-closedness for the moduli functor $\mathcal{S}_P^{sm}$ which parametrizes the stable smoothable foliated surface pairs. On the way, we also show a result on the invariance of plurigenera.

math.AG↗

arXiv2022

Fujita's conjecture for quasi-elliptic surfaces

We show that Fujita's conjecture is true for quasi-elliptic surfaces. Explicitly, for any quasi-elliptic surface $X$ and an ample line bundle $A$ on $X$, we have $K_X + tA$ is base point free for $t \geq 3$ and is very ample for $t \geq 4$.

math.AG↗

arXiv2022

Boundedness of minimal partial du Val resolutions of canonical surface foliations

In this paper, we prove the boundedness of foliated surfaces $(X,\mathscr{F})$ which are minimal partial du Val resolutions of canonical models $(X_c,\mathscr{F}_c)$ of general type. For applications, we show the boundedness of non-cusp singularities on canonical models of foliated surfaces of general type and the effective generation on the complement of the cusp singularities.

math.AG↗

arXiv2021

Log canonical foliation singularities on surfaces

We give a classification of the dual graphs of the exceptional divisors on the minimal resolutions of log canonical foliation singularities on surfaces. For an application, we show the set of foliated minimal log discrepancies for foliated surface triples satisfies the ascending chain condition and a Grauert-Riemenschneider type vanishing theorem for foliated surfaces with good log canonical foliation singularities.

math.AG↗