On extremal contractions of log canonical pairs

Abstract: The cone and contraction theorem holds for projective log canonical pairs. Let us consider an extremal contraction morphism of a log canonical pair. We prove that every irreducible component of the exceptional locus is uniruled. This result was first proved by Yujiro Kawamata for kawamata log terminal pairs. His proof uses a relative Kawamata--Viehweg vanishing theorem for projective bimeromorphic morphisms of complex analytic spaces and does not work for log canonical pairs. Our approach is based on the theory of quasi-log schemes and can be applied to more general settings. We need a semipositivity theorem coming from the theory of variations of mixed Hodge structure. We note that we do not use the minimal model program.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

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