Let X be a variety with terminal singularities of dimension n. We study local contractions f: X → Z supported by a ℚ-Cartier divisor of the type KX + τL, where L is an f-ample Cartier divisor and τ > 0 is a rational number. Equivalently, f is a Fano-Mori contraction associated to an extremal face in NE(X)KX+τL=0. We prove that, if τ > (n - 3) > 0, the general element X′ ϵ \L\ is a variety with at most terminal singularities. We apply this to characterize, via an inductive argument, some birational contractions as above with τ > (n - 3) > 0.
Local Fano-Mori contractions of high nef-value / M. Andreatta, L. Tasin. - In: MATHEMATICAL RESEARCH LETTERS. - ISSN 1073-2780. - 23:5(2016), pp. 1247-1262. [10.4310/MRL.2016.v23.n5.a1]
Local Fano-Mori contractions of high nef-value
L. Tasin
2016
Abstract
Let X be a variety with terminal singularities of dimension n. We study local contractions f: X → Z supported by a ℚ-Cartier divisor of the type KX + τL, where L is an f-ample Cartier divisor and τ > 0 is a rational number. Equivalently, f is a Fano-Mori contraction associated to an extremal face in NE(X)KX+τL=0. We prove that, if τ > (n - 3) > 0, the general element X′ ϵ \L\ is a variety with at most terminal singularities. We apply this to characterize, via an inductive argument, some birational contractions as above with τ > (n - 3) > 0.File | Dimensione | Formato | |
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