Geometry Seminar

University of Tor Vergata, Department of Mathematics

29th of November 2022, 14:30-15:30, room “Dal Passo”

Speaker

Andreas Knutsen

(University of Bergen)

Title

Severi varieties of Enriques surfaces

Abstract

Given a (smooth) projective (complex) surface S and a complete

linear (or algebraic) system of curves on S, one defines the Severi

varieties to be the (possibly empty) subvarieties parametrizing nodal

curves in the linear system, for any prescribed number of nodes. These

were originally studied by Severi in the case of the projective plane.

Afterwards, Severi varieties on other surfaces have been studied, mostly

rational surfaces, K3 surfaces and abelian surfaces, often in connection

with enumerative formulas computing their degrees.  Interesting

questions are nonemptiness, dimension, smoothness and irreducibility of

Severi varieties.

In this talk I will first give a general overview and then present

recent results about Severi varieties on Enriques surfaces, obtained

with Ciliberto, Dedieu and Galati, and the connection to a conjecture of

Pandharipande and Schmitt.