Let X be a projective variety with Q-factorial terminal singularities and let L be an ample Cartier divisor on X. We prove that if f is a birational contraction associated to an extremal ray R subset of <(NE(X))over bar> such that R center dot(K-X+(n-2)L)< 0, then f is a weighted blow-up of a smooth point. We then classify divisorial contractions associated to extremal rays R such that R center dot(K-X+rL)< 0, where r is a non-negative integer, and the fibres of f have dimension less than or equal to r+1.

Fano-Mori contractions of high length on projective varieties with terminal singularities / M. Andreatta, L. Tasin. - In: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6093. - 46:1(2014), pp. 185-196.

Fano-Mori contractions of high length on projective varieties with terminal singularities

L. Tasin
2014

Abstract

Let X be a projective variety with Q-factorial terminal singularities and let L be an ample Cartier divisor on X. We prove that if f is a birational contraction associated to an extremal ray R subset of <(NE(X))over bar> such that R center dot(K-X+(n-2)L)< 0, then f is a weighted blow-up of a smooth point. We then classify divisorial contractions associated to extremal rays R such that R center dot(K-X+rL)< 0, where r is a non-negative integer, and the fibres of f have dimension less than or equal to r+1.
Mathematics (all)
Settore MAT/03 - Geometria
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/638188
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