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 δ=0,…,pa(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.