A view on contractions of higher dimensional varieties

Abstract

In this paper we discuss some recent results about extremal contractions of complex algebraic varieties. These are proper surjective maps, φ: X Z, of normal varieties with connected fibers such that X has mild singularities (in particular X is Q-Gorenstein) and the anticanonical divisor of X is φ ample. It will appear on the Proceedings of AMS-SRI on Algebraic Geometry, Santa Cruz 1995.

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