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Birational rigidity of Fano varieties and field extensions

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Abstract

This note studies the behavior of birational rigidity and universal birational rigidity in extensions of algebraically closed fields.

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References

  1. C. Birkar, P. Cascini, C. D. Hacon, and J. McKernan, “Existence of Minimal Models for Varieties of Log General Type,” arXiv:math/0610203.

  2. I. A. Cheltsov, “Birationally Rigid Fano Varieties,” Usp. Mat. Nauk 60(5), 71–160 (2005) [Russ. Math. Surv. 60, 875–965 (2005)].

    MathSciNet  Google Scholar 

  3. I. Cheltsov, “Fano Varieties with Many Selfmaps,” Adv. Math. 217(1), 97–124 (2008).

    Article  MATH  MathSciNet  Google Scholar 

  4. A. Corti and M. Mella, “Birational Geometry of Terminal Quartic 3-folds. I,” Am. J. Math. 126(4), 739–761 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  5. A. Corti and M. Reid, “Foreword,” in Explicit Birational Geometry of 3-folds (Cambridge Univ. Press, Cambridge, 2000), LMS Lect. Note Ser. 281, pp. 1–20.

    Google Scholar 

  6. V. A. Iskovskikh, “Birational Rigidity of Fano Hypersurfaces in the Framework of Mori Theory,” Usp. Mat. Nauk 56(2), 3–86 (2001) [Russ. Math. Surv. 56, 207–291 (2001)].

    MathSciNet  Google Scholar 

  7. J. Kollár and S. Mori, “Classification of Three-Dimensional Flips,” J. Am. Math. Soc. 5(3), 533–703 (1992).

    Article  MATH  Google Scholar 

  8. J. Kollár, Rational Curves on Algebraic Varieties (Springer, Berlin, 1996), Ergebn. Math. Grenzgeb., 3. Flg. 32.

    Google Scholar 

  9. J. Kollár, K. E. Smith, and A. Corti, Rational and Nearly Rational Varieties (Cambridge Univ. Press, Cambridge, 2004), Cambridge Stud. Adv. Math. 92.

    MATH  Google Scholar 

  10. M. Mella, “Birational Geometry of Quartic 3-folds. II: The Importance of Being ℚ-Factorial,” Math. Ann. 330(1), 107–126 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  11. M. Rosenlicht, “Some Basic Theorems on Algebraic Groups,” Am. J. Math. 78, 401–443 (1956).

    Article  MATH  MathSciNet  Google Scholar 

  12. C. Shramov, “Birational Automorphisms of Nodal Quartic Threefolds,” arXiv: 0803.4348.

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  1. Princeton University, Princeton, NJ, 08544-1000, USA

    János Kollár

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  1. János Kollár
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Correspondence to János Kollár.

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Kollár, J. Birational rigidity of Fano varieties and field extensions. Proc. Steklov Inst. Math. 264, 96–101 (2009). https://doi.org/10.1134/S008154380901012X

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