Speaker: Jose Seade (National University of Mexico and Mexican Academy of Sciences)

Time: 16:00-17:00 p.m., Feb 17, 2025, GMT+8

Venue: Jingchunyuan, BICMR, PKU

Abstract: 

Let be an open neighborhood of Let  be an open neighborhood of in and holomorphic with a  critical point at ; set . Then  is an analytic variety with a possibly non-isolated singularity at. A classical way to study the geometry and topology of  is by looking at a local non-critical level , known as the Milnor fiber. And an also classical way to study the topology of  is by slicing it with the level surfaces  of some general linear form ;  or more generally with the level surfaces of another holomorphic function  which is “good” with respect to . This goes back to ideas of Thom in the 1960s and developed further by Lê Dũng Tráng, Teissier and others. In particular one has the celebrated Lê-Greuel formula for the Milnor number.(s) of some general linear form ℓ; or more generally with the level surfaces of another holomorphic function  which is “good” with respect to . This goes back to ideas of Thom in the 1960s and developed further by  Lê Dũng Tráng, Teissier and others. In particular one has the celebrated Lê-Greuel formula for the Milnor number.
In this talk we will revise these results and explain how to generalize these to functions on varieties with arbitrary singular locus.This is recent work with Lê Dũng Tráng and J. Nuño-Ballesteros.

Source: Beijing International Center for Mathematical Research, PKU