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On the Degree-1 Abel Map for Nodal Curves

  • Aldi Nestor de Souza
  • Frederico SercioEmail author
Article

Abstract

Let C be a nodal curve and L be an invertible sheaf on C. Let \(\alpha _{L}:C\dashrightarrow J_{C}\) be the degree-1 rational Abel map, which takes a smooth point \(Q\in C\) to \(\left[ m_{Q}\otimes L\right] \) in the Jacobian of C. In this work we extend \(\alpha _{L}\) to a morphism \(\overline{\alpha }_{L}:C\rightarrow \overline{J}_{E}^{P}\) taking values on Esteves’ compactified Jacobian for any given polarization E. The maps \(\overline{\alpha }_{L}\) are limits of Abel maps of smooth curves of the type \(\alpha _{L}\).

Keywords

Abel map Nodal curves 

Mathematics Subject Classification

14H50 

Notes

Acknowledgements

We would like to thank Marco Pacini, Juliana Coelho and Alex Abreu for introducing us to the subject and for helping us to prepare this article. We would like to thank the anonymous referee for detailed comments and suggestions that greatly helped improve the article.

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Copyright information

© Sociedade Brasileira de Matemática 2018

Authors and Affiliations

  1. 1.Universidade Federal de Mato GrossoCuiabáBrazil
  2. 2.Universidade Federal de Juiz de ForaJuiz de ForaBrazil

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