Degeneration of Intermediate Jacobians and the Torelli Theorem
Degeneration of Intermediate Jacobians and the Torelli Theorem
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中间雅可比矩阵的退化和托雷利定理
作者：
S. Basu;A. Dan;Inder Kaur
Mumford和Newstead将经典的Torelli定理推广到更高的秩，即，一条光滑的射影曲线X唯一地由X上稳定秩为2的丛的模空间的第二中间雅可比行列式确定，且具有固定的奇次行列式。本文证明了当X是具有一个结点的不可约结点曲线时的类似结果。作为副产品，我们得到了第二中间Jacobian的退化和相应的N '{e}罗恩模型的一类这样的模空间。
Mumford and Newstead generalized the classical Torelli theorem to higher rank i.e., a smooth, projective curve $X$ is uniquely determined by the second intermediate Jacobian of the moduli space of stable rank $2$ bundles on $X$, with fixed odd degree determinant. In this article we prove the analogous result in the case $X$ is an irreducible nodal curve with one node. As a byproduct, we obtain the degeneration of the second intermediate Jacobians and the associated N'{e}ron model of a family of such moduli spaces.