Oct

15

2024

When:
Tuesday, October 15, 2024

3:00 PM - 4:00 PM CT

Where: Lunt Hall, 104, 2033 Sheridan Road, Evanston, IL 60208 map it

Audience: Faculty/Staff - Student - Public - Post Docs/Docs - Graduate Students

Contact:
Yuchen Liu
(847) 491-5553

Group: Department of Mathematics: Algebraic Geometry Seminar

Category: Lectures & Meetings

**Title**: Algebraicity of Shafarevich maps and the Shafarevich conjecture

**Abstract**: For a normal complex algebraic variety X equipped with a complex representation V of its fundamental group, a Shafarevich map f:X->Y is a map which contracts precisely those algebraic subvarieties on which V has finite monodromy. Such maps were constructed for projective X by Eyssidieux, and recently have been constructed analytically in the quasiprojective case by Brunebarbe and Deng--Yamanoi, in both cases using techniques from non-abelian Hodge theory. In joint work with Y. Brunebarbe and J. Tsimerman, we show that these maps are algebraic. This is a generalization of the Griffiths conjecture on the algebraicity of images of period maps, and the proof critically uses o-minimal GAGA. We will also explain how the same techniques can be used to prove the Shafarevich conjecture in the "linear case", which puts strong restrictions on the complex analytic varieties that arise as universal covers of algebraic varieties admitting linear representations of their fundamental groups.