具有单个奇维度的环面超簇

约化超概形与环面超簇的组合学

Reduced superschemes and the combinatorics of toric supervarieties

本文通过重新定义约化超环与超概形，建立了环面超簇与装饰多面体扇之间的范畴等价，并利用装饰多胞体刻画了异构超格拉斯曼流形中的自然环面超簇。

On the Hodge group and invariant cycles of a simple Abelian variety with a stable reduction of odd toric rank

The semi-simplicity of the Hodge group is proved for a simple Abelian variety with a stable reduction of odd toric (reductive) rank. If, besides, the dimension of the Abelian variety is an odd integer, then the Hodge conjecture on algebraic cycles holds for it.

On the Hodge conjecture for hypersurfaces in toric varieties

We show that very general hypersurfaces in odd-dimensional simplicial projective toric varieties verifying a certain combinatorial property satisfy the Hodge conjecture (these include projective spaces). This gives a connection between the Oda conjecture and Hodge conjecture. We also give an explicit criterion which depends on the degree for very general hypersurfaces for the combinatorial condition to be verified.

环面Fano簇的积分与有理Gongyo指数之间的差距

On the gap between the integral and rational Gongyo indices of toric Fano varieties

本文研究环面Fano簇的有理与积分Gongyo指数之差，证明维数下界并确定等号情形，构造无穷正差距族，并证明所有正有理数均可作为差距出现。

环面簇中 Noether-Lefschetz 分量的渐近描述

An asymptotic description of the Noether-Lefschetz components in toric varieties

本文将 Noether-Lefschetz 分量理论推广到单纯环面簇中的拟光滑超曲面，证明小余维数分量渐近对应于可关联小 k 维子簇的超曲面，并推广了 Green 定理与 artinian Gorenstein 理想概念。

C型Richardson边界与奇维射影空间的Newton-Okounkov退化

Type C Richardson Boundaries and Newton-Okounkov Degenerations of Odd-Dimensional Projective Space

该研究对比奇维射影空间的两种镜像理论退化图景，计算C型边界与对应Laurent多项式，构造Newton–Okounkov体并验证半群等同性，还给出连接两类边界的秩一权退化。