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Rational connectedness of log $Q$-Fano varieties

Qi Zhang

Published 2004-08-23, updated 2005-01-31Version 3

In this paper, we give an affirmative answer to a conjecture in the Minimal Model Program. We prove that log $Q$-Fano varieties of dim $n$ are rationally connected. We also study the behavior of the canonical bundles under projective morphisms.

Comments: Minor modifications. To appear in J. reine angew. Math
Categories: math.AG
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