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Semistable modifications of families of curves and compactified Jacobians

Eduardo Esteves Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, Brazil Marco Pacini Instituto de Matemática, Universidade Federal Fluminense Rua Mário Santos Braga

Geometric Analysis and Geometric Topology mathscidoc:1701.01023

Arkiv for Matematik, 54, (1), 55-83, 2014.1
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.
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@inproceedings{eduardo2014semistable,
  title={Semistable modifications of families of curves and compactified Jacobians},
  author={Eduardo Esteves, and Marco Pacini},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203641824826093},
  booktitle={Arkiv for Matematik},
  volume={54},
  number={1},
  pages={55-83},
  year={2014},
}
Eduardo Esteves, and Marco Pacini. Semistable modifications of families of curves and compactified Jacobians. 2014. Vol. 54. In Arkiv for Matematik. pp.55-83. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203641824826093.
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