Nonemptiness of Severi varieties on Enriques surfaces

Abstract

Let $(S,L)$ be a general polarized Enriques surface, with $L$ not numerically 2-divisible. We prove the existence of regular components of all Severi varieties of irreducible $\delta$-nodal curves in the linear system $|L|$, with $0\le \delta \le p_a(L)-1$. 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.

34 pages. Minor changes, incorporating referee's corrections; final version appeared in Forum of Math

References in corpus (1)

• Severi varieties on blow--ups of the symmetric square of an elliptic curve

Cited by in corpus (4)

• Rational curves and Seshadri constants on Enriques surfaces
• Nodal rational curves on Enriques surfaces of base change type
• A note on elliptic curves on toric surfaces
• Limits of nodal surfaces and applications