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http://dx.doi.org/10.4134/BKMS.b160677

BIRATIONAL RIGIDITY IS NOT AN OPEN PROPERTY  

Cheltsov, Ivan (School of Mathematics University of Edinburgh Peter Guthrie Tait Road, King's Buildings Campus)
Grinenko, Mikhail (Steklov Institute of Mathematics)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.5, 2017 , pp. 1485-1526 More about this Journal
Abstract
We show that birational rigidity of Mori fibre spaces is not open in moduli.
Keywords
Fano variety; birational rigidity; complete intersection;
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1 M. Artin, Some numerical criteria of contractability of curves on algebraic surfaces, Amer. J. Math. 84 (1962), 485-496.   DOI
2 A. Corti, Singularities of linear systems and 3-fold birational geometry, Explicit birational geometry of 3-folds, 259-312, London Math. Soc. Lecture Note Ser., 281, Cambridge Univ. Press, Cambridge, 2000
3 V. Iskovskikh and A. Pukhlikov, Birational automorphisms of multidimensional algebraic manifolds, J. Math. Sci. 82 (1996), no. 4, 3528-3613.   DOI
4 M. Kawakita, Divisorial contractions in dimension three which contracts divisors to smooth points, Invent. Math. 145 (2001), no. 1, 105-119.   DOI
5 A. Pukhlikov, Essentials of the method of maximal singularities, Explicit birational geometry of 3-folds, 73-100, London Math. Soc. Lecture Note Ser., 281, Cambridge Univ. Press, Cambridge, 2000.
6 A. Pukhlikov, Birationally rigid varieties, Mathematical Surveys and Monographs 190, AMS, Providence, RI, 2013.
7 K. Shramov, $\mathbb{Q}$-factorial quartic threefolds, Sb. Math. 198 (2007), no. 7-8, 1165-1174.   DOI
8 A. Corti and M. Mella, Birational geometry of terminal quartic 3-folds I, Amer. J. Math. 126 (2004), no. 4, 739-761.   DOI