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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 .
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Nov 17, 2018
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