Weak boundedness theorems for canonically fibered Gorenstein minimal threefolds

Xiao's Conjecture on Canonically Fibered Surfaces

A canonically fibered surface is a surface whose canonical series maps it to a curve. Using Miyaoka-Yau inequality, A. Beauville proved that a canonically fibered surface has relative genus at most 5 when its geometric genus is sufficiently large. G. Xiao further conjectured that the relative genus cannot exceed 4. We give a proof of this conjecture.

三角规范纤维化曲面

Trigonal Canonically Fibered Surfaces

本文修复了相对亏格5的规范纤维化曲面的Xiao猜想证明中的漏洞，简化了原证明并改进了曲面几何亏格的界，同时将该方法推广至相对亏格3和4的曲面，获得了相应的Noether型不等式。

On canonically polarized Gorenstein 3-folds satisfying the Noether equality

We study canonically polarized Gorenstein $3$-folds with at most terminal singularities and satisfying $K_X^3=\frac 43p_g(X)-\frac {10}3$ and $p_g(X) \ge 7$. We characterize the canonical maps of such $3$-folds, describe a structure theorem for the locally factorial ones and completely classify the smooth ones. New examples of canonically polarized smooth $3$-folds with $K_X^3=\frac 43p_g(X)-\frac {10}3$ and $p_g(X) \ge 7$ are constructed. These examples are natural extensions of those constructed by M.~Kobayashi.

Analytic Isomorphisms of compressed local algebras

In this paper we consider Artin local K-algebras with maximal length in the class of Artin algebras with given embedding dimension and socle type. They have been widely studied by several authors, among others by Iarrobino, Fröberg and Laksov. If the local K-algebra is Gorenstein of socle degree 3, then the authors proved that it is canonically graded, i.e. analytically isomorphic to its associated graded ring. This unexpected result has been extended to compressed level K-algebras of socle degree 3 by A. De Stefani. In this paper we end the investigation proving that extremal Artin Gorenstein…

模尔紧化M_{1,n≤6}的积分柴环

Integral Chow rings of modular compactifications of $\mathcal{M}_{1,n\leq 6}$

本文计算了n≤6时所有仅参数化Gorenstein曲线及其光滑不同标记的模尔紧化的积分柴环，包括Deligne-Mumford、Schubert和Smyth紧化等，并研究了柴- Künneth生成性质及Getzler关系。

Logarithmic Kodaira-Akizuki-Nakano vanishing and Arakelov-Parshin boundedness for singular varieties

The article has two parts. The first part is devoted to proving a singular version of the logarithmic Kodaira-Akizuki-Nakano vanishing theorem of Esnault and Viehweg. This is then used to prove other vanishing theorems. In the second part these vanishing theorems are used to prove an Arakelov-Parshin type boundedness result for families of canonically polarized varieties with rational Gorenstein singularities.