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arXiv · 1503.05256

Unirationality of moduli spaces of special cubic fourfolds and K3 surfaces

Howard Nuer
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Abstract

We provide explicit descriptions of the generic members of Hassett's divisors $\mathcal C_d$ for relevant $18\leq d\leq 38$ and for $d=44$. In doing so, we prove that $\mathcal C_d$ is unirational for $18\leq d\leq 38,d=44$. As a corollary, we prove that the moduli space $\mathcal N_{d}$ of polarized K3 surfaces of degree $d$ is unirational for $d=14,26,38$. The case $d=26$ is entirely new, while the other two cases have been previously proven by Mukai.

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Howard Nuer. 2015-03-18. Unirationality of moduli spaces of special cubic fourfolds and K3 surfaces. https://arxiv.org/abs/1503.05256

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