A note on Nikulin surfaces and their moduli spaces

Abstract

We study a number of natural linear systems carried by any polarized Nikulin surface of genus g, determine their positivity and establish their Brill-Noether theory. As an application, we compute the classes of some natural effective divisors on the moduli space of Nikulin surfaces, relying upon recent work of Farkas and Rimányi.L m = L ⊗ e −m , m = 0, 1, 2, . . .