地点：海纳苑2幢204室

时间：3月23日，16:00 - 17:20

报告人：张希平 Xiping Zhang（同济大学）

摘要:  

Pretalk: Chern Classes on Singular Varieties

Abstract: The Poincaré–Hopf theorem states that the topological Euler characteristic of a compact complex manifold equals the degree of the Euler class of its tangent bundle. In this talk, we will review how this theorem extends to the singular setting, following the reformulation of Grothendieck and Deligne.

Research talk:   Betti Bounds for Hypersurfaces in Projective Varieties

Abstract: In this talk we will consider a degree $d$ hypersurface $Y$ in a $n$-dimensional projective variety $X$ and discuss the upper bound for the total sum of Betti numbers of $Y$. We show that this sum is bounded by $3\deg(X)\cdot d^n +C\cdot d^{n-1}$, where $C$ is an explicit constant given by the Chern-Schwartz-MacPherson class of $X$. When $X$ is a complete intersection this bound modifies to $\deg(X)\cdot d^n +C\cdot d^{n-1}$ and is asymptotically sharp with respect to $d$. This is a joint work with Xuanyu Pan and Dingxin Zhang.