Complete curves in the moduli space of polarized K3 surfaces and hyperKähler manifolds
Abstract
Building on an idea of Borcherds, Katzarkov, Pantev, and ShepherdBarron (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 hyperKähler manifolds of $\mathrm{K3}^{[n]}$type or $\mathrm{Kum}_n$type for all $n\ge 1$ and polarizations of various degrees and divisibilities.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 DOI:
 10.48550/arXiv.2108.00429
 arXiv:
 arXiv:2108.00429
 Bibcode:
 2021arXiv210800429D
 Keywords:

 Mathematics  Algebraic Geometry;
 14D20;
 14F08;
 14J28;
 14J42;
 14J60
 EPrint:
 20 pages. v2: fixed and clarified the computations for lower degrees