Polarizations on abelian subvarieties of principally polarized abelian varieties with dihedral group actions
Author
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Lange, Herbert
Author
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Rodríguez, Rubí E.
es_CL
Author
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Rojas, Anita M.
es_CL
Admission date
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2014-12-17T15:29:49Z
Available date
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2014-12-17T15:29:49Z
Publication date
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2014
Cita de ítem
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Math. Z. (2014) 276:397–420
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Identifier
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DOI 10.1007/s00209-013-1206-1
Identifier
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https://repositorio.uchile.cl/handle/2250/119842
General note
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Artículo de publicación ISI
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Abstract
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For any n > 2 we study the group algebra decomposition of an ([n/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 fs icosahedral curve of genus 5.
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Patrocinador
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The second author was supported by Fondecyt Grant 1100767, the third author by Fondecyt Grant 1100113.