Towards Bounding Complexity of a Minimal Model
Resource
Compositio Mathematica 138 (3): 245-260
Journal
Compositio Mathematica
Journal Volume
138
Journal Issue
3
Pages
245-260
Date Issued
2003
Date
2003
Author(s)
Abstract
We give some effectivity results in birational geometry. We provide an upper bound on the rational constant in Rationality Theorem in terms of certain intersection numbers, under an additional condition on the variety that it admits a divisorial contraction. One consequence is an explicit bound on the number of certain extremal rays. Our main result tries to construct from a given set of ample divisors H j on X with their intersection numbers b i , a certain set of ample divisors L j on X ' or X + where X ' or X + arises from a contraction or a flip, such that the corresponding intersection numbers of L j are uniformly bounded in terms of b i and the index of X . This gives a bound on the projective degree of a minimal model in special case.
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journal article
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