Complete curves in the moduli space of polarized K3 surfaces and hyper-K\"ahler manifolds

Olivier Debarre; Emanuele Macrì

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arXiv · 2108.00429

Complete curves in the moduli space of polarized K3 surfaces and hyper-K\"ahler manifolds

Olivier Debarre·Emanuele Macrì

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Abstract

Building on an idea of Borcherds, Katzarkov, Pantev, and Shepherd-Barron (who treated the case $e=14$), we prove that the moduli space of polarized K3 surfaces of degree $2e$ contains complete curves for all $e\geq 62$ and for some sporadic lower values of $e$ (starting at $14$). We also construct complete curves in the moduli spaces of polarized hyper-K\"ahler manifolds of $\mathrm{K3}^{[n]}$-type or $\mathrm{Kum}_n$-type for all $n\ge 1$ and polarizations of various degrees and divisibilities.

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BibTeX RIS

Olivier Debarre, Emanuele Macrì. 2021-08-01. Complete curves in the moduli space of polarized K3 surfaces and hyper-K\"ahler manifolds. https://arxiv.org/abs/2108.00429

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