Autoduality of compactified Jacobians for curves with plane singularities
Autoduality of compactified Jacobians for curves with plane singularities
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具有平面奇点的曲线的紧化雅可比行列式的自对偶性
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
D. Arinkin
中科院分区：
文献类型：
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作者：
D. Arinkin;D. Arinkin
设\(C\)为具有平面奇点的整射影曲线。考虑其雅可比簇\(J\)以及紧化雅可比簇\(J'\)。我们在\(J'\)上构造一个由\(J'\)参数化的科恩 - 麦克劳林层的平坦族\(P\)；在\(J\)上，族\(P\)是庞加莱线丛。我们证明由\(P\)给出的傅里叶 - 穆凯变换是\(J'\)的导出范畴的一个自等价。
Let C be an integral projective curve with planar singularities. Consider its Jacobian J and the compactified Jacobian J'. We construct a flat family P of Cohen-Macaulay sheaves on J' parametrized by J'; over J, the family P is the Poincare line bundle. We prove that the Fourier-Mukai transform given by P is an auto-equivalence of the derived category of J'.