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On the Degree-1 Abel Map for Nodal Curves

On the Degree-1 Abel Map for Nodal Curves Let C be a nodal curve and L be an invertible sheaf on C. Let $$\alpha _{L}:C\dashrightarrow J_{C}$$ α L : C ⤏ J C be the degree-1 rational Abel map, which takes a smooth point $$Q\in C$$ Q ∈ C to $$\left[ m_{Q}\otimes L\right] $$ m Q ⊗ L in the Jacobian of C. In this work we extend $$\alpha _{L}$$ α L to a morphism $$\overline{\alpha }_{L}:C\rightarrow \overline{J}_{E}^{P}$$ α ¯ L : C → J ¯ E P taking values on Esteves’ compactified Jacobian for any given polarization E. The maps $$\overline{\alpha }_{L}$$ α ¯ L are limits of Abel maps of smooth curves of the type $$\alpha _{L}$$ α L . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

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References (27)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Sociedade Brasileira de Matemática
Subject
Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/s00574-018-00127-8
Publisher site
See Article on Publisher Site

Abstract

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

Journal

Bulletin of the Brazilian Mathematical Society, New SeriesSpringer Journals

Published: Nov 17, 2018

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