تقرير
Alternating trilinear forms on a 9-dimensional space and degenerations of (3,3)-polarized Abelian surfaces
| العنوان: | Alternating trilinear forms on a 9-dimensional space and degenerations of (3,3)-polarized Abelian surfaces |
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| المؤلفون: | Gruson, Laurent, Sam, Steven V |
| المصدر: | Proc. Lond. Math. Soc. (3) 110 (2015), no. 3, 755-785 |
| سنة النشر: | 2013 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, 14D06, 14D22, 14K10, 15A72 |
| الوصف: | 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. Comment: 30 pages; v2: small corrections |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1112/plms/pdu050 |
| الوصول الحر: | http://arxiv.org/abs/1301.5276Test |
| رقم الانضمام: | edsarx.1301.5276 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1112/plms/pdu050 |
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