# Seminars & Colloquia Calendar

Algebra Seminar

## The Kodaira dimension of some moduli spaces of elliptic K3 surfaces

#### Giacomo Mezzedimi (Hannover)

Location:  https://rutgers.zoom.us/j/95075528338
Date & time: Wednesday, 07 October 2020 at 2:00PM - 3:00PM

Abstract: Let $$\mathcal{M}_{2k}$$ denote the moduli space of $$U\oplus \langle -2k\rangle$$-polarized K3 surfaces. Geometrically, the K3 surfaces in $$\mathcal{M}_{2k}$$ are elliptic and contain an extra curve class, depending on $$k\ge 1$$. I will report on a joint work with M. Fortuna and M. Hoff, in which we compute the Kodaira dimension of $$\mathcal{M}_{2k}$$ for almost all $$k$$: more precisely, we show that it is of general type if $$k\ge 220$$ and unirational if $$k\le 50, k$$ not in $$\{11,35,42,48\}$$. After introducing the general problem, I will compare the strategies used to obtain both results. If time permits, I will show some examples arising from explicit geometric constructions.

For the meeting password, email Ian at:
iacoley@math.rutgers.edu.

## Special Note to All Travelers

Directions: map and driving directions. If you need information on public transportation, you may want to check the New Jersey Transit page.

Unfortunately, cancellations do occur from time to time. Feel free to call our department: 848-445-6969 before embarking on your journey. Thank you.