2001/01/29 by V. Alexeev, V. A. Alexeev, Alexeev, V. +5 · 1 citation
Mathematics · Physics and Astronomy · #14D06 #14K10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #math.AG #msc:14D06 #msc:14K10
paper · pdf · doi:10.48550/arxiv.math/0101241
Final version, to appear in Crelle Journal. 51 pages, 15 *.eps pictures
openalex publication_date 2001/01/29 · arxiv created 2002/01/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (C,ι) be a stable curve with an involution. Following a classical construction one can define its Prym variety P, which in this case turns out to be a semiabelian group variety and usually not complete. In this paper we study the question whether there are ``good'' compactifications of P in analogy to compactified Jacobians. The answer to this question depends on whether we consider degenerations of principally polarized Prym varieties or degenerations with the induced (non-principal) polarization. We describe degeneration data of such degenerations. The main application of our theory lies in the case of degenerations of principally polarized Prym varieties where we ask whether such a degeneration depends on a given one-parameter family containing (C,ι) or not. This allows us to determine the indeterminacy locus of the Prym map.