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تسجيل مستخدم جديدComplete curves in the moduli space of polarized K3 surfaces and hyper-Kahler manifolds
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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 $egeq 62$ and for some sporadic lower values of $e$ (starting at $14$). We also construct complete curves in the moduli spaces of polarized hyper-Kahler manifolds of $mathrm{K3}^{[n]}$-type or $mathrm{Kum}_n$-type for all $nge 1$ and polarizations of various degrees and divisibilities.
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