Minimal Model Program with scaling and adjunction theory
Algebraic Geometry
2012-12-18 v2
Abstract
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.
Cite
@article{arxiv.1107.4878,
title = {Minimal Model Program with scaling and adjunction theory},
author = {Marco Andreatta},
journal= {arXiv preprint arXiv:1107.4878},
year = {2012}
}
Comments
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 Mathematics