Donagi, Ron The tetragonal construction. (English) Zbl 0491.14016 Bull. Am. Math. Soc., New Ser. 4, 181-185 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 ReviewsCited in 31 Documents MSC: 14H15 Families, moduli of curves (analytic) 14K10 Algebraic moduli of abelian varieties, classification 14H40 Jacobians, Prym varieties 32G20 Period matrices, variation of Hodge structure; degenerations 14H30 Coverings of curves, fundamental group Keywords:Prym variety; polarized abelian variety; moduli space; tetragonal construction; Andreotti-Mayer varieties; fibres of Prym map Citations:Zbl 0333.14013 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] A. Andreotti and A. L. Mayer, On period relations for abelian integrals on algebraic curves, Ann. Scuola Norm. Sup. Pisa (3) 21 (1967), 189 – 238. · Zbl 0222.14024 [2] Arnaud Beauville, Prym varieties and the Schottky problem, Invent. Math. 41 (1977), no. 2, 149 – 196. · Zbl 0333.14013 · doi:10.1007/BF01418373 [3] Arnaud Beauville, Variétés de Prym et jacobiennes intermédiaires, Ann. Sci. École Norm. Sup. (4) 10 (1977), no. 3, 309 – 391 (French). · Zbl 0368.14018 [4] C. Herbert Clemens, Double solids, Adv. in Math. 47 (1983), no. 2, 107 – 230. · Zbl 0509.14045 · doi:10.1016/0001-8708(83)90025-7 [5] Ron Donagi and Roy Smith, The degree of the Prym map onto the moduli space of five-dimensional abelian varieties, Journées de Géometrie Algébrique d’Angers, Juillet 1979/Algebraic Geometry, Angers, 1979, Sijthoff & Noordhoff, Alphen aan den Rijn — Germantown, Md., 1980, pp. 143 – 155. Ron Donagi and Roy Campbell Smith, The structure of the Prym map, Acta Math. 146 (1981), no. 1-2, 25 – 102. · Zbl 0538.14019 · doi:10.1007/BF02392458 [6] David Mumford, Prym varieties. I, Contributions to analysis (a collection of papers dedicated to Lipman Bers), Academic Press, New York, 1974, pp. 325 – 350. · Zbl 0299.14018 [7] Yu. I. Manin, Cubic forms, 2nd ed., North-Holland Mathematical Library, vol. 4, North-Holland Publishing Co., Amsterdam, 1986. Algebra, geometry, arithmetic; Translated from the Russian by M. Hazewinkel. · Zbl 0582.14010 [8] Sevin Recillas, Jacobians of curves with \?\textonesuperior \(_{4}\)’s are the Prym’s of trigonal curves, Bol. Soc. Mat. Mexicana (2) 19 (1974), no. 1, 9 – 13. · Zbl 0343.14012 [9] A. Tjurin, Geometry of the Poincaré theta-divisor of a Prym variety, Math. U. S. S. R. Izv. 9 (1975), 951-986. · Zbl 0339.14017 [10] W. Wirtinger, Untersuchugen über Thetafunctionen, Teubner, Berlin, 1895. · JFM 26.0514.01 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.