# Margherita Lelli-Chiesa: Genus two curves on abelian surfaces

**Time: **
Wed 2020-02-05 13.15 - 15.00

**Location: **
Kräftriket, house 6, room 306

**Lecturer: **
Margherita Lelli-Chiesa (Università Roma Tre)

### Abstract

Let (*S*,*L*) be a general (*d*_{1},*d*_{2})-polarized abelian surfaces. The minimal geometric genus of any curve in the linear system |*L*| is two and there are finitely many curves of such genus. In analogy with Chen's results concerning rational curves on K3 surfaces, it is natural to ask whether all such curves are nodal. In the seminar I will prove that this holds true if and only if *d*_{2} is not divisible by 4. In the cases where *d*_{2} is a multiple of 4, I will construct curves in |*L*| having a triple, 4-tuple or 6-tuple point, and show that these are the only types of unnodal singularities a genus 2 curve in |*L*| may acquire. This is joint work with A. L. Knutsen.