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arXiv · 2110.15819

Explicit constructions of K3 surfaces and unirational Noether-Lefschetz divisors

Michael Hoff·Giovanni Staglianò
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Abstract

We provide methods to construct explicit examples of $K3$ surfaces. This leads to unirational constructions of Noether--Lefschetz divisors inside the moduli space of $K3$ surfaces of genus $g$. We implement Mukai's unirationality construction of the moduli spaces of $K3$ surfaces of genus $g\in\{6,\dots, 10, 12\}$, and we also present a new constructive proof of the unirationality of the moduli space of $K3$ surfaces of genus $11$. Furthermore, we show the existence of three unirational hypersurfaces in any moduli space of $K3$ surfaces of genus $g$.

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Michael Hoff, Giovanni Staglianò. 2021-10-29. Explicit constructions of K3 surfaces and unirational Noether-Lefschetz divisors. https://arxiv.org/abs/2110.15819

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