On Abel maps of stable curves

2006/03/20 by Lucia Caporaso, Caporaso, Lucia, Eduardo Esteves +1
Mathematics · #14H10 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14H10

paper · pdf · doi:10.48550/arxiv.math/0603476

32 pages

arxiv created 2006/03/20 · arxiv updated 2009/12/01

Abstract

We construct Abel maps for a stable curve X. Namely, for each one-parameter deformation of X with regular total space, and every integer d>0, we construct by specialization a map α^d_X from the smooth locus of X^d to the moduli scheme of balanced line bundles on semistable curves over X. For d=1, we show that α¹_X naturally extends over X, and does not depend on the choice of the deformation; we give a precise description of when it is injective.

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