## Algebraic Geometry Seminar

Francois Greer

Michigan State

Elliptic surfaces over an elliptic base

**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.

Monday November 11, 2024 at 3:00 PM in 636 SEO