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# 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 6ā10, 2015*, Proceedings of Symposia in Pure Mathematics,**95**, Providence, RI: American Mathematical Society, pp. 1ā32, MR 3727495

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