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 all Severi varieties irreducible nodal curves in linear system $|L|$ , that is, for any number nodes $\delta =0, \ldots p_a(L)-1$ . This solves classical open problem and gives positive answer to recent conjecture Pandharipande–Schmitt, under additional condition non-2-divisibility.