On the degree-1 Abel map for nodal curves

Abstract

Let $C$ be a nodal curve and $L$ be an invertible sheaf on $C$. Let ${\alpha }_L:C⇢J_C$ 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 ${\overline{\alpha }}_L:C\to {\overline{J}}_E^P$ 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 ${\alpha }_L$.

26 pages, 5 figures, comments are welcome

References in corpus (2)

• Semistable modifications of families of curves and compactified Jacobians
• The degree-2 Abel-Jacobi map for nodal curves - II