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# A One-Dimensional Family of $K3$ Surfaces with a $\Z_4$ Action

Published:2009-12-01
Printed: Dec 2009
• Michela Artebani
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## Abstract

The minimal resolution of the degree four cyclic cover of the plane branched along a GIT stable quartic is a $K3$ surface with a non symplectic action of $\Z_4$. In this paper we study the geometry of the one-dimensional family of $K3$ surfaces associated to the locus of plane quartics with five nodes.
 Keywords: genus three curves, $K3$ surfaces
 MSC Classifications: 14J28 - $K3$ surfaces and Enriques surfaces 14J50 - Automorphisms of surfaces and higher-dimensional varieties 14J10 - Families, moduli, classification: algebraic theory

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