Unirational moduli spaces of some elliptic K3 surfaces

Abstract

We show that the moduli space of $U\oplus ⟨-2k⟩$-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.

17 pages

References in corpus (1)

• The Kodaira dimension of some moduli spaces of elliptic K3 surfaces