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The Prym-standard mapping of an algebraic curve. (Spanish) Zbl 0569.14013

Let X be a smooth nonsingular complete irreducible algebraic curve over \({\mathbb{C}}\) and the genus of X is \(\geq 4\). Let \(K_ X\) be its canonical class and \(\eta \in Pic_ 0(X)\) be such an element that \(\eta\) \(\neq 0\), \(2\eta =0\). Denote by \(w_{\eta}: X\to p^{g-2}\) the rational map defined by the sheaf of Prym differentials \(K_ X(\eta)=K_ X\otimes \eta\). The purpose of the paper is a detailed study of the map \(w_{\eta}\) in the case when it is not biregular and X is a hyperelliptic or elliptic-hyperelliptic curve and, especially, the genus of X is equal to 4.
Reviewer: V.L.Popov

MSC:

14H45 Special algebraic curves and curves of low genus
14E05 Rational and birational maps
14K20 Analytic theory of abelian varieties; abelian integrals and differentials
14H52 Elliptic curves
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