Polarizations on abelian subvarieties of principally polarized abelian varieties with dihedral group actions
نویسندگان
چکیده
For any n ≥ 2 we study the group algebra decomposition of an ([ 2 ] + 1)dimensional family of principally polarized abelian varieties of dimension n with an action of the dihedral group of order 2n. For any odd prime p, n = p and n = 2p we compute the induced polarization on the isotypical components of these varieties and some other distinguished subvarieties. In the case of n = p the family contains a one-dimensional family of Jacobians. We use this to compute a period matrix for Klein’s icosahedral curve of genus 5.
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