Degenerations of Prym varieties

Details Degenerations of Prym varieties Degenerations of Prym varieties

2001-01-29

arxiv.org/abs/math/0101241v2

Mathematics

Algebraic Geometry

Final version, to appear in Crelle Journal. 51 pages, 15 *.eps pictures

Scientific paper

Let $(C,\iota)$ 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 $(C,\iota)$ or not. This allows us to determine the indeterminacy locus of the Prym map.

Affiliated with

Also associated with

No associations

Rating

Degenerations of Prym varieties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Degenerations of Prym varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Degenerations of Prym varieties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-279902