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Degenerations of Prym varieties

V. Alexeev·Ch. Birkenhake·K. Hulek
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Abstract

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.

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BibTeXRIS

V. Alexeev, Ch. Birkenhake, K. Hulek. 2002-01-08. Degenerations of Prym varieties. https://arxiv.org/abs/math/0101241

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