Summary: FanoMori Contractions
M. Andreatta J.A. Wi'sniewski
Universit`a di Trento, Italy
University of Warsaw, Poland
[AW1] On contractions of smooth varieties,
to appear on Journal of Algebraic Geometry.
[AW2] A view on contractions of higher dimensional varieties,
to appear on the Proceedings of Santa Cruz 1995.
Internet: www.science.unitn.it/~ andreatt
A contraction ' : X ! Z is a proper map of normal irreducible
varieties with connected fibers.
We study the case X smooth; F denotes a fiber.
The contraction ' is called FanoMori (or also extremal) if the
anticanonical divisor \GammaK X is 'ample.
The map can be birational or of fiber type, i.e. dimX ? dimZ.
The exceptional locus E of a birational contraction ' is the smallset
subset of X such that ' is an isomorphism on X n E.
If codimE – 2 then ' is called small.