Index 1 covers of log terminal surface sigularities

Etale covers of Kawamata log terminal spaces and their smooth loci

Working with a singular variety X, one is often interested in comparing the set of etale covers of X with that of its smooth locus X_reg. More precisely, one may ask: What are the obstructions to extend finite etale covers of X_reg to all of X? How do the etale fundamental groups of X and of its smooth locus compare? For projective varieties with Kawamata log terminal (klt) singularities we answer these questions in part. The main result of this paper asserts that there are no infinite towers of finite morphisms over a klt base variety where all morphisms are etale in codimension one, but bran…

Étale fundamental groups of Kawamata log terminal spaces, flat sheaves, and quotients of Abelian varieties

Given a quasi-projective variety X with only Kawamata log terminal singularities, we study the obstructions to extending finite étale covers from the smooth locus $X_{\mathrm{reg}}$ of $X$ to $X$ itself. A simplified version of our main results states that there exists a Galois cover $Y \rightarrow X$, ramified only over the singularities of $X$, such that the étale fundamental groups of $Y$ and of $Y_{\mathrm{reg}}$ agree. In particular, every étale cover of $Y_{\mathrm{reg}}$ extends to an étale cover of $Y$. As first major application, we show that every flat holomorphic bundle defined on $…

强 $F$-正则与对数终端奇点的 Gorenstein 判据

A Gorenstein criterion for strongly $F$-regular and log terminal singularities

本文在反典范覆盖 Noetherian 的条件下证明 Hirose–Watanabe–Yoshida 猜想，并将阈值判据推广到正规 $F$-纯与对数典范奇点的拟 Gorenstein 判定。

关于 Galois 拟平展覆盖下弦性动机的行为

On the behavior of stringy motives under Galois quasi-étale covers

本文研究 Galois 拟平展覆盖下弦性动机的下降行为，证明其下降并在分歧时严格，进而将 KLT 奇点基本群有限性归结为 DCC 性质，并给出曲面及对数终端奇点的无特征证明。

Rational curves on fibered varieties

Let $X$ be a projective variety with log terminal singularities and vanishing augmented irregularity. In this paper we prove that if $X$ admits a relatively minimal genus one fibration then it does contain a subvariety of codimension one covered by rational curves contracted by the fibration. We then focus on the case of varieties with numerically trivial canonical bundle and we discuss several consequences of this result.

可接受的HYM度量在klt KE变种上的应用以及大反canonical K稳定变种的MY等式

Admissible HYM metrics on klt KE varieties and the MY equality for big anticanonical K-stable varieties

本文研究了Kähler-Einstein变种上反射sheaf的稳定性、K稳定变种的Miyaoka-Yau不等式等式以及holomorphic向量包的semistability性质。