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This article is cited in 9 scientific papers (total in 9 papers)
The intermediate Jacobian of the double covering of $P^3$ branched at a quartic
A. S. Tikhomirov
Abstract:
In this paper we study the intermediate Jacobian $J_3(X)$ of a double covering $X$ of $P^3$ branched at a smooth quartic which does not contain projective lines. We prove an analogue of the Riemann theorem for the Poincare's divisor of the intermediate Jacobian $J_3(X)$, the global Torelli theorem for $X$, and the nonrationality of $X$.
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Mathematics of the USSR-Izvestiya, 1981, 17:3, 523–566
Bibliographic databases:
  
UDC:
512.776
MSC: Primary 14E20, 14J30, 14K30; Secondary 14J15, 14J25, 14C30, 14E22, 14E35, 14M20, 14N05, 3
Received: 23.04.1980
Citation:
A. S. Tikhomirov, “The intermediate Jacobian of the double covering of $P^3$ branched at a quartic”, Izv. Akad. Nauk SSSR Ser. Mat., 44:6 (1980), 1329–1377; Math. USSR-Izv., 17:3 (1981), 523–566
Citation in format AMSBIB
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\pages 1329--1377
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\transl
\jour Math. USSR-Izv.
\yr 1981
\vol 17
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\pages 523--566
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http://mi.mathnet.ru/eng/izv1966 http://mi.mathnet.ru/eng/izv/v44/i6/p1329
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Erratum
This publication is cited in the following articles:
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A. S. Tikhomirov, “The Fano surface of the Veronese double cone”, Math. USSR-Izv., 19:2 (1982), 377–443
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D. G. Markushevich, “Numerical invariants of families of lines on some Fano varieties”, Math. USSR-Sb., 44:2 (1983), 239–260
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A. S. Tikhomirov, “Singularities of the theta divisor of the intermediate Jacobian of a double cover of $P^3$ of index two”, Math. USSR-Izv., 21:2 (1983), 355–373
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I. A. Cheltsov, “Birationally superrigid cyclic triple spaces”, Izv. Math., 68:6 (2004), 1229–1275
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V. V. Przyjalkowski, I. A. Cheltsov, K. A. Shramov, “Hyperelliptic and trigonal Fano threefolds”, Izv. Math., 69:2 (2005), 365–421
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A. V. Pukhlikov, “Birationally rigid varieties. I. Fano varieties”, Russian Math. Surveys, 62:5 (2007), 857–942
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A. V. Pukhlikov, “Birational geometry of Fano double spaces of index two”, Izv. Math., 74:5 (2010), 925–991
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A. V. Pukhlikov, “Birational geometry of higher-dimensional Fano varieties”, Proc. Steklov Inst. Math., 288, suppl. 2 (2015), S1–S150
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Marcello Bernardara, Gonçalo Tabuada, “From semi-orthogonal decompositions to polarized intermediate Jacobians via Jacobians of noncommutative motives”, Mosc. Math. J., 16:2 (2016), 205–235
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