95 research outputs found
Minimal Model Program with scaling and adjunction theory
Let (X,L) be a quasi polarized pairs, i.e. X is a normal complex projective
variety and L is a nef and big line bundle on it. We study, up to birational
equivalence, the positivity (nefness) of the adjoint bundles K_X + rL for high
rational number r. For this we run a Minimal Model Program with scaling
relative to the divisor K_X +rL. We give some applications, namely the
classification up to birational equivalence of quasi polarized pairs with
sectional genus 0,1 and of embedded projective varieties X < P^N with degree
smaller than 2codim(X) +2.Comment: 12 pages. Proposition 3.6 of the previous version was incomplete.
Some proofs have been shortened. The paper will be published on International
Journal of Mathematic
Fano-Mori contractions of high length on projective varieties with terminal singularities
Let X be a projective variety with 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 such that
R.(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.(K_X+rL)<0, where r is a non-negative rational number, and the fibres of f
have dimension less or equal to r+1.Comment: 12 pages. We fixed some lemmas and improved the exposition. To appear
in the Bulletin of the London Mathematical Societ
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