Algebraic varieties of dimension three whose hyperplane sections are Enriques surfaces
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 12 (1985) no. 1, p. 43-80
@article{ASNSP_1985_4_12_1_43_0,
     author = {Conte, A. and Murre, J. P.},
     title = {Algebraic varieties of dimension three whose hyperplane sections are Enriques surfaces},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 12},
     number = {1},
     year = {1985},
     pages = {43-80},
     zbl = {0612.14041},
     mrnumber = {818801},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1985_4_12_1_43_0}
}
Conte, A.; Murre, J. P. Algebraic varieties of dimension three whose hyperplane sections are Enriques surfaces. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 12 (1985) no. 1, pp. 43-80. http://www.numdam.org/item/ASNSP_1985_4_12_1_43_0/

[1] M. Artin, Som numerical criteria for contractability of curves on algebraic surfaces, Amer. J. Math., 84 (1962), pp. 485-496. | MR 146182 | Zbl 0105.14404

[2] A. Beauville, Surfaces algébriques complexes, Astérisque, 54, Paris, 1978. | MR 485887 | Zbl 0394.14014

[3] S. Bloch - J.P. Murre, On the Chow group of certain types of Fano threefolds, Compositio Math., 39 (1979), pp. 47-105. | Numdam | MR 539001 | Zbl 0426.14018

[4] F. Conforto, Le superficie razionali, Zanichelli, Bologna, 1939. | JFM 65.0714.03 | Zbl 0021.05306

[5] A. Conte - J.P. Murre, Three-dimensional algebraic varieties whose hyperplane sections are Enriques surfaces, Institut Mittag-Leffler, Report no. 10, 1981.

[6] A. Conte - A. Verra, Varietà aventi come sezioni iperpiane superficie di Enriques, to appear.

[7] F. Cossec, Projective models of Enriques surfaces, Math. Ann., 265 (1983), pp. 283-334. | MR 721398 | Zbl 0501.14021

[8] P. Du Val, On rational surfaces whose prime sections are canonical curves, Proc. London Math. Soc., 35 (1933), pp. 1-13. | JFM 59.0649.01 | Zbl 0006.22101

[9] D. Epema, Surfaces with canonical curves as hyperplane sections, Indagationes Math., 45 [1983), pp. 173-84. | MR 705424 | Zbl 0532.14018

[10] G. Fano, Nuove ricerche sulle congruenze di rette del 30 ordine, Mem. Accad. Sci. Torino, 50 (1901), pp. 1-79. | JFM 33.0685.02

[11] G. Fano, Sulle varietà algebriche a tre dimensioni le cui sezioni iperpiane sono superficie di genere zero e bigenere uno, Memorie società dei XL, 24 (1938), pp. 41-66. | JFM 65.1403.02 | Zbl 0022.07702

[12] L. Godeaux, Sur les variétés algébriques à trois dimensions dont les sections hyperplanes sont des surfaces de genre zéro et de bigenre un, Bull. Acad. Belgique, Cl. des Sci., 14 (1933), pp. 134-140. | JFM 59.0652.03 | Zbl 0007.42201

[13] R. Hartshorne, Algebraic Geometry, Springer-Verlag, New York, 1977. | MR 463157 | Zbl 0367.14001

[14] V.A. Iskovskih, Fano threefolds I and II, Izv. Akad. Nauk SSSR, 41 (1977), pp. 516-562, resp. 42 (1978), pp. 506-549 (and english translation). | MR 463151 | Zbl 0407.14016

[15] V.A. Iskovskih, Anticanonical models of three-dimensional algebraic varieties, in: Itogi Nauki i Tekniki, Sov. Pr. Mat., 12 (1979), pp. 59-157; engl. transl. in J. Soviet Math., 13 (1980), pp. 745-814. | MR 537685 | Zbl 0428.14016

[16] M. Letizia, Sistemi lineari completi su superficie di Enriques, Ann. di Mat., 126 (1980), pp. 267-283. | MR 612363 | Zbl 0469.14003

[17] T. Matsusaka, On the theorem of Castelnuovo-Enriques, Natur. Sc. Rep., Ochanomizo Univ., 4 (1953), pp. 164-171. | MR 63691 | Zbl 0056.14601

[18] D. Mumford, Topology of normal singularities and a criterion for simplicity, Publ. IHES, 9 (1961), pp. 229-246. | Numdam | Zbl 0108.16801

[19] D. Mumford, Pathologies III, Amer. J. Math., 89 (1967), pp. 94-104. | MR 217091 | Zbl 0146.42403

[20] L. Picco-Botta - A. Verra, The nonrationality of the Enriques threefold, Compositio Math., 48 (1983), pp. 167-184. | Numdam | MR 700002 | Zbl 0508.14032

[21] M. Reid, Hyperelliptic linear systems on a K3-surface, J. London Math. Soc., 13 (1976), pp. 427-437. | MR 435082 | Zbl 0338.14009

[22] B. Saint-Donat, Projective models of K3-surfaces, Amer. J. Math., 96 (1972), pp. 602-639. | MR 364263 | Zbl 0301.14011

[23] C. Segre, Étude des différentes surfaces du 4e ordre à conique double ou cuspidale (générale ou décomposée) considérées comme des projections de l'intersection de deux variétés quadratiques de l'espace à quatre dimensions, Math. Ann., 29 (1884), pp. 313-444. | JFM 16.0596.01 | MR 1510288

[24] A.N. Tjurin, Five lectures on three-dimensional varieties, Russian Math. Surveys, 30 (1975), pp. 51-105. | Zbl 0263.14012

[25] A. Weil, Foundations of Algebraic Geometry, Am. Math. Soc. Colloq. Publ., 29, revised and enlarged edition, Providence, 1962. | MR 144898 | Zbl 0168.18701

[26] A. Weil, Sur les critères d'équivalence en géométrie algébrique, Math. Ann., 128 (1954), pp. 95-127. | MR 65219 | Zbl 0057.13002

[27] O. Zariski, Algebraic Surfaces, 2nd suppl. ed., Ergebnisse, 61, Springer-Verlag. Heidelberg, 1971. | MR 469915 | Zbl 0219.14020

[28] O. Zariski, An introduction to the theory of algebraic surfaces, Lecture Notes in Math., 83, Springer, Berlin, 1969. | MR 263819 | Zbl 0177.49001

[29] O. Zariski, Complete linear systems on normal varieties and a generalization of a lemma of Enriques-Severi, Ann. of Math., 55 (1962), pp. 552-592. | MR 48857 | Zbl 0047.14803