Unirational moduli spaces of some elliptic K3 surfaces
Abstract
We show that the moduli space of $U\oplus \langle 2k \rangle$polarized K3 surfaces is unirational for $k \le 50$ and $k \notin \{11,35,42,48\}$, and for other several values of $k$ up to $k=97$. Our proof is based on a systematic study of the projective models of elliptic K3 surfaces in $\mathbb{P}^n$ for $3\le n \le 5$ containing either the union of two rational curves or the union of a rational and an elliptic curve intersecting at one point.
 Publication:

arXiv eprints
 Pub Date:
 August 2020
 DOI:
 10.48550/arXiv.2008.12077
 arXiv:
 arXiv:2008.12077
 Bibcode:
 2020arXiv200812077F
 Keywords:

 Mathematics  Algebraic Geometry;
 14J15;
 14J28 (Primary) 14J27;
 14Q10 (Secondary)
 EPrint:
 17 pages