Symplectic leaves in projective spaces of bundle extensions

IF 1.5 1区 数学 Q1 MATHEMATICS
Alexandru Chirvasitu
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引用次数: 0

Abstract

Fix a stable degree-n rank-k bundle F on a complex elliptic curve for (coprime) 1k<n3. We identify the symplectic leaves of the Poisson structure introduced independently by Polishchuk and Feigin-Odesskii on Pn1PExt1(F,O) as precisely the loci classifying extensions 0OEF0 with E fitting into a fixed isomorphism class, verifying a claim of Feigin-Odesskii. We also classify the bundles E which do fit into such extensions in geometric/combinatorial terms, involving their Harder-Narasimhan polygons introduced by Shatz.
束扩展射影空间中的辛叶
在复椭圆曲线上固定一个稳定度-n阶-k束F,当(素)1≤k<;n≥3时。在Pn−1 × PExt1(F,O)上,我们确定了由Polishchuk和Feigin-Odesskii独立引入的泊松结构的辛叶正是对扩展0→O→E→F→0进行分类的座,其中E拟合为一个固定的同构类,验证了Feigin-Odesskii的一个论断。我们还对符合这种扩展的束E进行了几何/组合分类,包括Shatz引入的Harder-Narasimhan多边形。
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来源期刊
Advances in Mathematics
Advances in Mathematics 数学-数学
CiteScore
2.80
自引率
5.90%
发文量
497
审稿时长
7.5 months
期刊介绍: Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.
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