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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Fine compactified Jacobians of reduced curves
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by Margarida Melo, Antonio Rapagnetta and Filippo Viviani PDF
Trans. Amer. Math. Soc. 369 (2017), 5341-5402 Request permission

Abstract:

To every singular reduced projective curve $X$ one can associate many fine compactified Jacobians, depending on the choice of a polarization on $X$, each of which yields a modular compactification of a disjoint union of a finite number of copies of the generalized Jacobian of $X$. We investigate the geometric properties of fine compactified Jacobians focusing on curves having locally planar singularities. We give examples of nodal curves admitting nonisomorphic (and even nonhomeomorphic over the field of complex numbers) fine compactified Jacobians. We study universal fine compactified Jacobians, which are relative fine compactified Jacobians over the semiuniversal deformation space of the curve $X$. Finally, we investigate the existence of twisted Abel maps with values in suitable fine compactified Jacobians.
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Additional Information
  • Margarida Melo
  • Affiliation: Departamento de Matemática, Universidade de Coimbra, Largo D. Dinis, Apartado 3008, 3001 Coimbra, Portugal – and – Dipartimento di Matematica, Università Roma Tre, Largo S. Leonardo Murialdo 1, 00146 Roma, Italy
  • MR Author ID: 803065
  • Email: mmelo@mat.uc.pt
  • Antonio Rapagnetta
  • Affiliation: Dipartimento di Matematica, Università di Roma II - Tor Vergata, 00133 Roma, Italy
  • Email: rapagnet@mat.uniroma2.it
  • Filippo Viviani
  • Affiliation: Dipartimento di Matematica, Università Roma Tre, Largo S. Leonardo Murialdo 1, 00146 Roma, Italy
  • MR Author ID: 761968
  • Email: viviani@mat.uniroma3.it
  • Received by editor(s): June 15, 2014
  • Received by editor(s) in revised form: May 8, 2015, and August 24, 2015
  • Published electronically: March 6, 2017
  • © Copyright 2017 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 369 (2017), 5341-5402
  • MSC (2010): Primary 14D20, 14H40, 14H60; Secondary 14H20, 14F05, 14K30, 14B07
  • DOI: https://doi.org/10.1090/tran/6823
  • MathSciNet review: 3646765