Abstract
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.
Funding Statement
The first author was supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico, Processo no. 304259/2010-1, by Coordenção de Aperfeiçoamento de Pessoal de Nível Superior, Processo no. 4155-13-0 and by Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro, Processo no. E-26/102.979/2011. The second author was supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico, Processos no. 300714/2010-6 e 304044/2013-0.
Citation
Eduardo Esteves. Marco Pacini. "Semistable modifications of families of curves and compactified Jacobians." Ark. Mat. 54 (1) 55 - 83, April 2016. https://doi.org/10.1007/s11512-015-0220-4
