DOI QR코드

DOI QR Code

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)
  • 투고 : 2016.08.17
  • 심사 : 2017.02.24
  • 발행 : 2017.09.30

초록

We show that birational rigidity of Mori fibre spaces is not open in moduli.

키워드

참고문헌

  1. M. Artin, Some numerical criteria of contractability of curves on algebraic surfaces, Amer. J. Math. 84 (1962), 485-496. https://doi.org/10.2307/2372985
  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. A. Corti and M. Mella, Birational geometry of terminal quartic 3-folds I, Amer. J. Math. 126 (2004), no. 4, 739-761. https://doi.org/10.1353/ajm.2004.0026
  4. V. Iskovskikh and A. Pukhlikov, Birational automorphisms of multidimensional algebraic manifolds, J. Math. Sci. 82 (1996), no. 4, 3528-3613. https://doi.org/10.1007/BF02363913
  5. M. Kawakita, Divisorial contractions in dimension three which contracts divisors to smooth points, Invent. Math. 145 (2001), no. 1, 105-119. https://doi.org/10.1007/s002220100144
  6. 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.
  7. A. Pukhlikov, Birationally rigid varieties, Mathematical Surveys and Monographs 190, AMS, Providence, RI, 2013.
  8. K. Shramov, $\mathbb{Q}$-factorial quartic threefolds, Sb. Math. 198 (2007), no. 7-8, 1165-1174. https://doi.org/10.1070/SM2007v198n08ABEH003878