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arXiv · 2004.08719

Monodromy of rational curves on K3 surfaces of low genus

Sailun Zhan
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Abstract

In many situations, the monodromy group of enumerative problems will be the full symmetric group. In this paper, we study a similar phenomenon on the rational curves in $|\mathcal{O}(1)|$ on a generic K3 surface of fixed genus over $\mathbb{C}$ as the K3 surface varies. We prove that when the K3 surface has genus $g$, $1\leq g\leq 3$, the monodromy group is the full symmetric group.

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Sailun Zhan. 2020-04-18. Monodromy of rational curves on K3 surfaces of low genus. https://doi.org/10.1016/j.jpaa.2022.107021

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