摘要翻译：
本文在切线系数矩阵最多秩为2的附加假设下，证明了van Geemen和van der Geer的$\gamma_{00}$猜想。这个假设是雅可比的，因此我们的结果给出了在所有主极化阿贝尔变体中的雅可比轨迹的刻划。这一证明是通过半生成三分形（即存在与库默变体在一点上相切而在另一点上相交的线）来归结为雅可比的（更强的）刻划，这是Krichever在证明Welters的三分形猜想的过程中证明的。
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英文标题：
《A special case of the $\Gamma_{00}$ conjecture》
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作者：
Samuel Grushevsky
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最新提交年份：
2010
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  In this paper we prove the $\Gamma_{00}$ conjecture of van Geemen and van der Geer, under the additional assumption that the matrix of coefficients of the tangent has rank at most 2. This assumption is satisfied by Jacobians, and thus our result gives a characterization of the locus of Jacobians among all principally polarized abelian varieties.   The proof is by reduction to the (stronger version of the) characterization of Jacobians by semidegenerate trisecants, i.e. by the existence of lines tangent to the Kummer variety at one point and intersecting it in another, proven by Krichever in the course of his proof of the Welters' trisecant conjecture.
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PDF链接：
https://arxiv.org/pdf/0804.0525