Francois Greer : Elliptic surfaces over an elliptic base

Posted by Philip Engel , part of the Algebraic Geometry Seminar.

At

Nov. 11, 2024, 3 p.m.

In

636 SEO

Abstract

Elliptic surfaces are a fairly well understood class of complex projective surfaces. They come with two discrete invariants, $g$ and $d$, both nonnegative integers. I will discuss some new results (joint with P. Engel, A. Ward, and Y. Zhang) about the moduli space and Hodge theory of elliptic surfaces with $(g,d)=(1,1)$. While they have Kodaira dimension one, they behave like K3 surfaces in many respects, and they provide an interesting test case for the Hodge Conjecture in dimension 4.