Simpson Jacobians of generalized tree-like curves

2001/07/23 by Ana Cristina Lopez, Lopez, Ana Cristina
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG

paper · pdf · doi:10.48550/arxiv.math/0107161

Latex file with two figures

arxiv created 2001/07/23 · openalex publication_date 2001/07/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The compactified Jacobian of any projective curve X is defined as the Simpson moduli space of torsion free rank one degree d sheaves that are semistable with respect to a fixed polarization H on X. In this paper we give explicitly the structure of this compactified Simpson Jacobian in the case where X is a generalized tree-like curve, i.e., a projective, reduced and connected curve such that the intersection points of its irreducible components are disconnecting ordinary double points. We prove that it is isomorphic to the product of the compactified Jacobians of a certain degree d_i of its components C_i, where the degrees d_i depend on d, H and on the particular structure of the curve. We find also necessary and sufficient conditions for the existence of stable points which allow us to study the variation of these Simpson Jacobians as the polarization H changes.

Citations

• Compactifying the relative Jacobian over families of reduced curves
• Counting rational curves on K3 surfaces

Related

• Simpson Jacobians of reducible curves
• Compactified Jacobians of curves with spine decompositions
• Extending the Torelli map to alternative compactifications of the moduli space of curves
• A new class of compactified Jacobians for families of reduced curves
• Compactifications of the universal Jacobian over curves with marked points