Special divisors on curves on K3 surfaces carrying an Enriques involution
Marco Ramponi
TL;DR
This paper investigates the properties of minimal degree pencils on curves on K3 surfaces with an Enriques involution, revealing that their gonality is primarily determined by the genus 1 fibrations of the surface.
Contribution
It provides new insights into the gonality of curves on K3 surfaces with involutions, linking it to the surface's genus 1 fibrations.
Findings
Gonality of curves is governed by genus 1 fibrations.
Minimal degree pencils are studied on curves with involution.
Results connect surface fibrations to curve properties.
Abstract
We study the pencils of minimal degree on the smooth curves lying on a K3 surface X which carries a fixed-point free involution. Generically, the gonality of these curves is totally governed by the genus 1 fibrations of X
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