Nonemptiness of severi varieties on enriques surfaces

Abstract

Let $(S,L)$ be a general polarised Enriques surface, with L not numerically 2-divisible. We prove the existence of regular components of all Severi varieties of irreducible nodal curves in the linear system $|L|$ , that is, for any number of nodes $\delta =0, \ldots , p_a(L)-1$ . This solves a classical open problem and gives a positive answer to a recent conjecture of Pandharipande–Schmitt, under the additional condition of non-2-divisibility.

Keywords

• 14H20
• 14J28
• 14D06
• 14H10
• 14J10