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arXiv · 2008.12077

Unirational moduli spaces of some elliptic K3 surfaces

Mauro Fortuna·Michael Hoff·Giacomo Mezzedimi
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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.

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Mauro Fortuna, Michael Hoff, Giacomo Mezzedimi. 2020-08-27. Unirational moduli spaces of some elliptic K3 surfaces. https://doi.org/10.1007/s00229-022-01455-2

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