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• W3101592013 abstract "We give a detailed analysis of the semisimple elements, in the sense of Vinberg, of the third exterior power of a 9-dimensional vector space over an algebraically closed field of characteristic different from 2 and 3. To a general such element, one can naturally associate an Abelian surface X, which is embedded in 8-dimensional projective space. We study the combinatorial structure of this embedding and explicitly recover the genus 2 curve whose Jacobian variety is X. We also classify the types of degenerations of X that can occur. Taking the union over all Abelian surfaces in Heisenberg normal form, we get a 5-dimensional variety which is a birational model for a genus 2 analogue of Shioda's modular surfaces. We find determinantal set-theoretic equations for this variety and present some additional equations which conjecturally generate the radical ideal." @default.
• W3101592013 created "2020-11-23" @default.
• W3101592013 creator A5053662840 @default.
• W3101592013 creator A5066686947 @default.
• W3101592013 date "2015-02-10" @default.
• W3101592013 modified "2023-09-27" @default.
• W3101592013 title "Alternating trilinear forms on a nine-dimensional space and degenerations of (3, 3)-polarized Abelian surfaces" @default.
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• W3101592013 doi "https://doi.org/10.1112/plms/pdu050" @default.
• W3101592013 hasPublicationYear "2015" @default.
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