Maximal variation of curves on K3 surfaces
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Publication:6367335
DOI10.2140/TUNIS.2022.4.443arXiv2105.04787MaRDI QIDQ6367335
Daniel Huybrechts, Yajnaseni Dutta
Publication date: 11 May 2021
Abstract: We prove that curves in a non-primitive, base point free, ample linear system on a K3 surface have maximal variation. The result is deduced from general restriction theorems applied to the tangent bundle. We also show how to use specialisation to spectral curves to deduce information about the variation of curves contained in a K3 surface more directly. The situation for primitive linear systems is not clear at the moment. However, the maximal variation holds in genus two and can, in many cases, be deduced from a recent result of van Geemen and Voisin confirming a conjecture due to Matsushita.
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