Abstract:
We show that a general divisor of bidegree (2,M) in P1×PM for M⩾4 is a birationally rigid variety and that the group of its birational automorphisms consists of two elements.
\Bibitem{Sob01}
\by I.~V.~Sobolev
\paper On a series of birationally rigid varieties with a~pencil of Fano hypersurfaces
\jour Sb. Math.
\yr 2001
\vol 192
\issue 10
\pages 1543--1551
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\crossref{https://doi.org/10.1070/SM2001v192n10ABEH000605}
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This publication is cited in the following 13 articles:
Johannes Nicaise, John Christian Ottem, “Tropical degenerations and stable rationality”, Duke Math. J., 171:15 (2022)
A. V. Pukhlikov, “Birationally rigid Fano fibre spaces. II”, Izv. Math., 79:4 (2015), 809–837
A. V. Pukhlikov, “Birational geometry of higher-dimensional Fano varieties”, Proc. Steklov Inst. Math., 288, suppl. 2 (2015), S1–S150
A. V. Pukhlikov, “Birationally rigid varieties. II. Fano fibre spaces”, Russian Math. Surveys, 65:6 (2010), 1083–1171
Aleksandr V. Pukhlikov, Cohomological and Geometric Approaches to Rationality Problems, 2010, 275
Pukhlikov A.V., “Birational geometry of algebraic varieties with a pencil of Fano cyclic covers”, Pure Appl. Math. Q., 5:2 (2009), 641–700
A. V. Pukhlikov, “Birationally rigid varieties. I. Fano varieties”, Russian Math. Surveys, 62:5 (2007), 857–942
A. V. Pukhlikov, “Birationally rigid varieties with a pencil of Fano double covers. III”, Sb. Math., 197:3 (2006), 335–368
Pukhlikov A.V., “Birational geometry of algebraic varieties with a pencil of Fano complete intersections”, Manuscripta Math., 121:4 (2006), 491–526
A. V. Pukhlikov, “Birational geometry of Fano direct products”, Izv. Math., 69:6 (2005), 1225–1255
A. V. Pukhlikov, “Birationally rigid varieties with a pencil of double Fano covers. I”, Sb. Math., 195:7 (2004), 1039–1071
A. V. Pukhlikov, “Birationally rigid varieties with a pencil of Fano double covers. II”, Sb. Math., 195:11 (2004), 1665–1702
A. V. Pukhlikov, “Birationally rigid iterated Fano double covers”, Izv. Math., 67:3 (2003), 555–596