A combinatorial property of generic immersions of curves

奇辛部分旗流形族的曲线邻域与组合性质$\u0026#x1D4AA;$

Curve neighborhoods and combinatorial property $\mathcal{O}$ for a family of odd symplectic partial flag manifolds

该研究针对奇辛部分旗流形族$\u200b\mbox{IF}(1,2;E)$，完整刻画其任意Schubert簇的$d$次曲线邻域不可约分支、研究格结构，证明了猜想$\u0026#x1D4AA;$的组合版本。

Algebraic and combinatorial rank of divisors on finite graphs

We study the algebraic rank of a divisor on a graph, an invariant defined using divisors on algebraic curves dual to the graph. We prove it satisfies the Riemann-Roch formula, a specialization property, and the Clifford inequality. We prove that it is at most equal to the (usual) combinatorial rank, and that equality holds in many cases, though not in general.

Uniqueness property for spherical homogeneous spaces

Let G be a connected reductive group. Recall that a G-variety X is called spherical if X is normal and a Borel subgroup of G has an open orbit on X. To a spherical homogeneous G-space one assigns certain combinatorial invariants: the weight lattice, the valuation cone and the set of B-stable prime divisors. We prove that two spherical homogeneous spaces with the same combinatorial invariants are equivariantly isomorphic. Further, we show how to recover the group of G-equivariant automorphisms from these invariants.

线性复形的关联与组合性质

Incidence and Combinatorial Properties of Linear Complexes

本文推广极性概念，以关联几何方式完全描述$h$-子空间的线性复形，并利用广义极性得到射影空间直线集合的非几何展形划分，该划分具有特征性的线性性质。

The Gorenstein property for projective coordinate rings of the moduli of parabolic $\mathrm{SL}_2$-principal bundles on a smooth curve

Using combinatorial methods, we determine that a projective coordinate ring of the moduli of parabolic principal $\mathrm{SL}_2$-bundles on a marked projective curve is not Gorenstein when the genus and number of marked points are greater than $1$.

多射影空间中点集的算术Cohen-Macaulay性质研究

On the arithmetically Cohen-Macaulay property for sets of points in multiprojective spaces

该研究先提出推广的$(\n\bstar_n)$-性质刻画$(\n\bP^1)^n$中有限点集的ACM性质，后勘误修正：ACM是$(\n\bstar_n)$的充分条件，仅$n=3$时必要，$n=4$存在反例。