The global indices of log Calabi-Yau varieties --A supplement to Fujino's paper: The indices of log canonical singularities--

A supplement to Fujino's paper: On isolated log canonical singularities with index one

Let $E$ be the essential part of the exceptional locus of a good resolution of an isolated, log canonical singularity of index one. We describe the dimension of the dual complex of $E$ in terms of the Hodge type of $H^{n-1}(E, O_E)$, which is one of the main results of the paper [1] of Fujino. Our proof uses only an elementary classical method, while Fujino's argument depends on the recent development in minimal model theory.

关于 Fujino 通过周期映射研究典范丛公式工作的一点注记

A Remark on Fujino's work on the canonical bundle formula via period maps

本文推广 Fujino 的典范丛公式结果，证明一般纤维为温和奇点本原辛簇时模部分半丰，并利用 c1 平凡簇结构理论将 K-平凡簇族情形归约到更弱 Calabi–Yau 条件。

The Euler Characteristic Formula for Logarithmic Minimal Degenerations of Surfaces with Kodaira Dimension Zero and its application to Calabi-Yau Threefolds with a pencil

In this paper, the Euler characteristic formula for projective logarithmic minimal degenerations of surfaces with Kodaira dimension zero over a 1-dimensional complex disk is proved under a reasonable assumption and as its application, the singularity of logarithmic minimal degenerations are determined in the abelian or hyperelliptic case. By globalizing this local analysis of singular fibres via generalized canonical bundle formulae due to Fujino-Mori, we bound the number of singular fibres of abelian fibred Calabi-Yau threefolds from above,which was previously done by Oguiso in the potentiall…

Variation of numerical dimension of singular hermitian line bundles

The purpose of this paper is to give two supplements for vanishing theorems: One is a relative version of the Kawamata-Viehweg-Nadel type vanishing theorem, which is obtained from an observation for the variation of the numerical dimension of singular hermitian line bundles. The other is an analytic injectivity theorem for log canonical pairs on surfaces, which can be seen as a partial answer for Fujino's conjecture.

On the motive of Kummer varieties associated to $Γ_1(7)$ - Supplement to the paper: The modularity of certain non-rigid Calabi-Yau threefolds (by R. Livné and N. Yui)

In their paper Livné and Yui (math.AG/0304497) discuss several examples of non-rigid Calabi-Yau varieties which admit semi-stable K3-fibrations with 6 singular fibres over a base which is a rational modular curve. They also establish the modularity of the L-function of these examples. The purpose of this note is to point out that the examples which were listed in their paper, but which do not lead to semi-stable fibrations, are still modular in the sense that their L-function is associated to modular forms. We treat the case associated to the group Gamma_1(7) in detail, but our technique also …

Calabi-Yau叶状结构与形变

Calabi-Yau Foliations and Deformations

该研究聚焦Calabi-Yau型叶状结构的三类形变，证明对应Kuranishi空间的光滑性与乘积结构，并建立f-形变与补叶状结构tr-形变的对应关系，丰富了叶状结构形变理论。