Semistable modifications of families of curves and compactified Jacobians
Semistable modifications of families of curves and compactified Jacobians
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曲线族的半稳定修正和紧致雅可比行列式
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
M. Pacini
中科院分区：
文献类型：
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作者：
E. Esteves;M. Pacini
给定一个节点曲线族，它的一个半稳定修改是另一个曲线族，它是由在原始曲线族的某些曲线的某些节点上插入任何给定长度的有理曲线链而得到的。我们给出了无挠秩1层与可逆层的比较定理。我们应用它们表明，有函同构的紧化的相对雅可比族的节点曲线通过Caporaso的方法和那些通过Pandharipande的方法构建。
Given a family of nodal curves, a semistable modification of it is another family made up of curves obtained by inserting chains of rational curves of any given length at certain nodes of certain curves of the original family. We give comparison theorems between torsion-free, rank-1 sheaves in the former family and invertible sheaves in the latter. We apply them to show that there are functorial isomorphisms between the compactifications of relative Jacobians of families of nodal curves constructed through Caporaso’s approach and those constructed through Pandharipande’s approach.