Detecting flat normal cones using Segre classes

On the influence of the Segre Problem on the Mori cone of blown-up surfaces

We propose a generalization of SHGH Conjectures to a smooth projective surface Y: the so called Segre Problem. The study of linear systems on Y can be translated in terms of the Mori cone of the blow up $X = Bl_r Y$ at $r$ general points. Generalizing a result by de Fernex, we prove that if Segre Problem holds true, then a part of the Mori cone of $X$ does coincide with a part of the positive cone of $X$.

Lorentzian多项式、Segre类与凸多面体锥的伴随多项式

Lorentzian polynomials, Segre classes, and adjoint polynomials of convex polyhedral cones

本文研究了余体积多项式与Lorentzian多项式的关系，证明其具有M-凸支撑和截面对数凹性，并将其应用于全局生成丛的Chern类和射影空间乘积子概形的Segre类，最后证明了凸多面体锥的伴随多项式是余体积多项式。

A relative Segre zeta function

The choice of a homogeneous ideal in a polynomial ring defines a closed subscheme $Z$ in a projective space as well as an infinite sequence of cones over $Z$ in progressively higher dimension projective spaces. Recent work of Aluffi introduces the Segre zeta function, a rational power series with integer coefficients which captures the relationship between the Segre class of $Z$ and those of its cones. The goal of this note is to define a relative version of this construction for closed subschemes of projective bundles over a smooth variety. If $Z$ is a closed subscheme of such a projective bu…

Higher Codimension Cycles on the Hilbert Scheme of Three Points on the Projective Plane

In this paper, we study the higher codimensional cycle structure of the Hilbert scheme of three points in the projective plane. In particular, we compute all Chern (and Segre) classes of all tautological bundles on it and compute the nef (effective) cones of cycles in codimensions 2 and 3 (dimensions 2 and 3).

射影辛空间中包含对合锥的超曲面

Hypersurfaces containing involutive cones in projective symplectic spaces

该研究刻画了射影辛空间中包含对合锥的超曲面，通过关联空间和 Segre 类积分计算关联次数，并给出了双有理性的充分判据及特殊维数下的闭式公式。

检测复解析芽中的快速消失环（以及检测内部度量锥形的芽）

Detecting fast vanishing loops in complex-analytic germs (and detecting germs that are inner metrically conical)

研究了纯维数n≥2的既约复解析芽中同调环的快速消失问题，利用判别式和覆盖数据给出了充要条件，并据此判定芽是否具有内部度量锥形（IMC）性质。