A note on Nikulin surfaces and their moduli spaces

TL;DR

This paper investigates linear systems on polarized Nikulin surfaces, analyzing their positivity and Brill-Noether properties, and computes classes of effective divisors on their moduli spaces, advancing understanding of their geometric structure.

Contribution

It provides new results on the positivity and Brill-Noether theory of linear systems on Nikulin surfaces and computes divisor classes on their moduli spaces.

Findings

Determined positivity of certain linear systems on Nikulin surfaces.

Established Brill-Noether theory for these linear systems.

Computed classes of effective divisors on the moduli space of Nikulin surfaces.

Abstract

We study some natural linear systems carried by polarized Nikulin surfaces of genus g. We determine their positivity and establish their Brill-Noether theory. As an application, we compute the class of some natural effective divisors associated to these linear systems on the moduli space of Nikulin surfaces, relying upon recent work of Farkas and Rim\'{a}nyi.