التفاصيل البيبلوغرافية
| العنوان: |
Alternating trilinear forms on a nine-dimensional space and degenerations of (3, 3)-polarized Abelian surfaces. |
| المؤلفون: |
Gruson, Laurent1 laurent.gruson@math.uvsq.fr, Sam, Steven V.2 svs@math.berkeley.edu |
| المصدر: |
Proceedings of the London Mathematical Society. Mar2015, Vol. 110 Issue 3, p1-785. 31p. |
| مصطلحات موضوعية: |
*TRILINEAR forms, *DIMENSIONAL analysis, *ABELIAN functions, *GEOMETRIC surfaces, *PROJECTIVE spaces, *COMBINATORICS |
| مستخلص: |
We give a detailed analysis of the semisimple elements, in the sense of Vinberg, of the third exterior power of a nine-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 eight-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 five-dimensional variety which is a birational model for a genus 2 analog 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. [ABSTRACT FROM AUTHOR] |
| قاعدة البيانات: |
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