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The tetragonal construction. (English) Zbl 0491.14016


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

Citations:

Zbl 0333.14013
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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.
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