2018/02/04 by Knutsen, Andreas Leopold, Lelli-Chiesa, Margherita, Verra, Alessandro · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1802.01201
Primitively polarized genus g Nikulin surfaces (S,M,H) are of two types, that we call standard and non-standard depending on whether the lattice embedding ℤ[H] ⊕⊥ N ⊂ \rmPic(S) is primitive. Here H is the genus g polarization and N is the Nikulin lattice. We concentrate on the non-standard case, which only occurs in odd genus. In particular, we study the birational geometry of the moduli space of non-standard Nikulin surfaces of genus g and prove its rationality for g=7,11 and the existence of a rational double cover of it when g=9. Furthermore, if (S,M,H) is general in the above moduli space and (C,M|C) is a general Prym curve in |H|, we determine the dimension of the family of non-standard Nikulin surfaces of genus g containing (C, M|C) for 3≤ g≤ 11; this completes the study of the Prym-Nikulin map initiated in our previous work.