Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

A special configuration of $12$ conics and generalized Kummer surfaces

Abstract : A generalized Kummer surface $X$ obtained as the quotient of an abelian surface by a symplectic automorphism of order 3 contains a $9\mathbf{A}_{2}$-configuration of $(-2)$-curves. Such a configuration plays the role of the $16\mathbf{A}_{1}$-configurations for usual Kummer surfaces. In this paper we construct $9$ other such $9\mathbf{A}_{2}$-configurations on the generalized Kummer surface associated to the double cover of the plane branched over the sextic dual curve of a cubic curve. The new $9\mathbf{A}_{2}$-configurations are obtained by taking the pullback of a certain configuration of $12$ conics which are in special position with respect to the branch curve, plus some singular quartic curves. We then construct some automorphisms of the K3 surface sending one configuration to another. We also give various models of $X$ and of the generic fiber of its natural elliptic pencil.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

https://hal.inria.fr/hal-03046892
Contributor : Xavier Roulleau <>
Submitted on : Tuesday, December 8, 2020 - 4:00:52 PM
Last modification on : Monday, December 28, 2020 - 3:54:02 PM

Links full text

Identifiers

  • HAL Id : hal-03046892, version 1
  • ARXIV : 2004.11421

Collections

Citation

David Kohel, Xavier Roulleau, Alessandra Sarti. A special configuration of $12$ conics and generalized Kummer surfaces. 2020. ⟨hal-03046892⟩

Share

Metrics

Record views

13