Speaker: Prof. Xia Liao (Huaqiao University, China)
Date: 15 July (Mon.) 2019, 11:00-12:00
Place: AORC Seminar Room (SKKU, General Studies Bd. 3F)
Talk1: basic examples of free divisors
Abstract:
Free divisors arise as a common theme in quite a few distinct geometric contexts. Originally, free divisors were found and defined in the context of studying the versal deformation of isolated complete intersection singularities. Later, the theory of free divisors found use in the combinatorial study of hyperplane arrangements. More recently, examples of free divisors are found in the study of quiver representations. I will show the audience some elementary examples of free divisors in these 3 contexts, to convince them that free divisor is indeed an interesting subject for mathematicians.
Date: 16 July (Tue.) 2019, 11:00-12:00
Place: AORC Seminar Room (SKKU, General Studies Bd. 3F)
Talk2: Chern classes of logarithmic vector fields for free divisors
Abstract:
Let $X$ be a nonsingular algebraic variety over \mathbb{C}, let $D$ be a divisor, and let $U = X \setminus D$ be its complement in $X$. It is well known that when $D$ is a simple normal crossing divisor, the cohomology of $U$ can be understood by the logarithmic vector fields along $D$. This fact is called logarithmic comparison theorem (LCT). Surprisingly, LCT is still true for locally quasi-homogeneous free divisors. We will explain that LCT implies an identity concerning the Chern class of logarithmic vector fields along $D$, and then we will show some applications of this identity.