Margherita Lelli-Chiesa: Genus two curves on abelian surfaces
Time: Wed 2020-02-05 13.15 - 15.00
Location: Kräftriket, house 6, room 306
Participating: Margherita Lelli-Chiesa (Università Roma Tre)
Let (S,L) be a general (d1,d2)-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 d2 is not divisible by 4. In the cases where d2 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.