Bracho, J.; Recillas, S. The Prym-standard mapping of an algebraic curve. (Spanish) Zbl 0569.14013 An. Inst. Mat., Univ. Nac. Autòn. Méx. 21, 105-127 (1981). 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 Keywords:genus equal to 4; complete irreducible algebraic curve; canonical class; rational map; Prym differentials; hyperelliptic curve PDFBibTeX XMLCite \textit{J. Bracho} and \textit{S. Recillas}, An. Inst. Mat., Univ. Nac. Autón. Méx. 21, 105--127 (1981; Zbl 0569.14013)