Genus 2 curve configurations on Fano surfaces

Details Genus 2 curve configurations on Fano surfaces Genus 2 curve configurations on Fano surfaces

2010-02-24

arxiv.org/abs/1002.4467v1

Mathematics

Algebraic Geometry

15 pages

Scientific paper

We study the configurations of genus 2 curves on the Fano surfaces of cubic threefolds. We establish a link between some involutive automorphisms acting on such a surface S and genus 2 curves on S. We give a partial classification of the Fano surfaces according to the automorphism group generated by these involutions and determine the configurations of their genus 2 curves. We study the Fano surface of the Klein cubic threefold for which the 55 genus 2 curves generate a rank 25=h^{1,1} index 2 subgroup of the N\'eron-Severi group.

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