Abundance conjecture: Difference between revisions

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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]\displaystyle{ X }[/math] with Kawamata log terminal singularities over a field [math]\displaystyle{ k }[/math] if the canonical bundle [math]\displaystyle{ K_X }[/math] is nef, then [math]\displaystyle{ K_X }[/math] is semi-ample.

Important cases of the abundance conjecture have been proven by Caucher Birkar.[1]

References

  1. Birkar, Caucher (2012). "Existence of log canonical flips and a special LMMP". Publications Mathématiques de l'IHÉS 115: 325–368. doi:10.1007/s10240-012-0039-5.