Abundance conjecture

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In algebraic geometry, the abundance conjecture is a conjecture in birational geometry, more precisely in the minimal model program, stating that for every projective variety <math>X</math> with Kawamata log terminal singularities over a field <math>k</math> if the canonical bundle <math>K_X</math> is nef, then <math>K_X</math> is semi-ample.

References[edit source | edit]

  • KollĆ”r, JĆ”nos; Mori, Shigefumi (1998), Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, 134, Cambridge University Press, Conjecture 3.12, p. 81, ISBN 978-0-521-63277-5, MR 1658959
  • Lehmann, Brian (2017), "A snapshot of the minimal model program" (PDF), in Coskun, Izzet; de Fernex, Tommaso; Gibney, Angela (eds.), Surveys on recent developments in algebraic geometry: Papers from the Bootcamp for the 2015 Summer Research Institute on Algebraic Geometry held at the University of Utah, Salt Lake City, UT, July 6ā€“10, 2015, Proceedings of Symposia in Pure Mathematics, 95, Providence, RI: American Mathematical Society, pp. 1ā€“32, MR 3727495

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