We study a number of natural linear systems carried by any polarized Nikulin surface of genus g. We determine their positivity and establish their Brill-Noether theory. Relying upon recent work of Farkas and Rim\'{a}nyi, we compute the class of some natural effective divisors associated to these linear systems on the moduli space of Nikulin surfaces, in this way obtaining --for any genus g-- roughly $\sqrt{g/2}$ relations in its tautological ring. 查看全文>>