Singularities of Severi Varieties on K3 Surfaces

par Xi Chen (University of Alberta)

jeudi 20 avr. 2023, 10:30 → 11:30 Europe/Paris

salle 207 bâtiment 1R2 (Institut de Mathématiques de Toulouse)

For a general polarized K3 surface (X,L) and g > 0, we prove that
after fixing g-1 general points, every curve of genus g in |L| passing
through these g-1 points has at worst a cusp. This implies that the
Severi variety parameterizing curves of genus g in |L| is smooth in
codimension 1. Together with Serre's criterion, we can prove that the
Severi variety is normal. If we further know it is connected, then we
can conclude it is irreducible. This is work in progress, joint with
Xiaotian Chang.