Partial Degree Formulae for Plane Offset Curves

Equivariant Chern-Schwartz-MacPherson classes in partial flag varieties: interpolation and formulae

Consider the natural torus action on a partial flag manifold $Fl$. Let $Ω_I\subset Fl$ be an open Schubert variety, and let $c^{sm}(Ω_I)\in H_T^*(Fl)$ be its torus equivariant Chern-Schwartz-MacPherson class. We show a set of interpolation properties that uniquely determine $c^{sm}(Ω_I)$, as well as a formula, of `localization type', for $c^{sm}(Ω_I)$. In fact, we proved similar results for a class $κ_I\in H_T^*(Fl)$ --- in the context of quantum group actions on the equivariant cohomology groups of partial flag varieties. In this note we show that $c^{SM}(Ω_I)=κ_I$.

$\partial\bar\partial$-性质的双亚纯不变性与 blow-up 公式 I：反例与导出范畴方法

Bimeromorphic invariance of $\partial\bar\partial$-property and blow-up formulae I: counterexamples and derived category approach

本文通过构造反例否定 $\partial\bar\partial$-引理的遗传性，并建立导出 blow-up 公式，引入相对性质与判据，揭示经典公式的局限。

Degree Formulae for Grassmann Bundles, II

Let $X$ be a non-singular quasi-projective variety over a field, and let $\mathcal E$ be a vector bundle over $X$. Let $\mathbb G_X({d}, \mathcal E)$ be the Grassmann bundle of $\mathcal E$ over $X$ parametrizing corank $d$ subbundles of $\mathcal E$ with projection $π: {\mathbb G_X({d}, \mathcal E)} \to X$, and let $ \mathcal Q \gets π^*\mathcal E$ be the universal quotient bundle of rank $d$. In this article, a closed formula for $π_{*}\operatorname{ch} (\det \mathcal Q)$, the push-forward of the Chern character of the Plücker line bundle $\det \mathcal Q$ by $π$ is given in terms of the Seg…

Hilbert模形式中零 genus 曲线的部分Hassé不变量

Partial Hasse invariants for genus zero curves in Hilbert modular varieties

本文研究了Hilbert模形式中零 genus 曲线的部分Hassé不变量的特征零提升，并通过计算Teichmüller曲线得到类似Deuring的公式。