Abundance conjecture

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 with Kawamata log terminal singularities over a field if the canonical bundle is nef, then is semi-ample.


  • Kollár, János; 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 6–10, 2015, Proceedings of Symposia in Pure Mathematics, 95, Providence, RI: American Mathematical Society, pp. 1–32, MR 3727495
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