Seminario di algebra e geometria
ore
16:00
presso Aula Arzelà
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.