紧化Jacobian的Fourier-Mukai和自对偶性I
Fourier-Mukai and autoduality for compactified Jacobians. I
摘要：
对于每一个奇异的约化的射影曲线X，我们可以联系到，遵循E。Esteves，许多精细的紧化雅可比矩阵，取决于X上的极化的选择，其中每一个产生X的广义雅可比矩阵的不交并的模紧化。证明了对具有局部平面奇点的约化曲线，从X的广义雅可比矩阵的导出范畴到X的任意细紧化雅可比矩阵的导出范畴的Poincare层的积分（或Fourier-Mukai）核变换是完全忠实的，推广了D. Arinkin在积分曲线的情况下。因此，我们证明了X的广义雅可比矩阵与X的任何细紧化雅可比矩阵的Picard方案的恒等式的连通分支之间存在正则同构（称为自对偶），并且在任何细紧化雅可比矩阵上代数等价和数值等价是一致的，推广了Arinkin，Esteves，Gagne '，Kleiman，Rocha，Sawon的结果.本文包含一个附录中，我们解释如何解释我们的工作可以解释鉴于朗兰兹对偶的希格斯包提出的Donagi-Pantev。
英文摘要：
To every singular reduced projective curve X one can associate, following E. Esteves, many fine compactified Jacobians, depending on the choice of a polarization on X, each of which yields a modular compactification of a disjoint union of the generalized Jacobian of X. We prove that, for a reduced curve with locally planar singularities, the integral (or Fourier-Mukai) transform with kernel the Poincare' sheaf from the derived category of the generalized Jacobian of X to the derived category of any fine compactified Jacobian of X is fully faithful, generalizing a previous result of D. Arinkin in the case of integral curves. As a consequence, we prove that there is a canonical isomorphism (called autoduality) between the generalized Jacobian of X and the connected component of the identity of the Picard scheme of any fine compactified Jacobian of X and that algebraic equivalence and numerical equivalence coincide on any fine compactified Jacobian, generalizing previous results of Arinkin, Esteves, Gagne', Kleiman, Rocha, Sawon. The paper contains an Appendix in which we explain how our work can be interpreted in view of the Langlands duality for the Higgs bundles as proposed by Donagi-Pantev.
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