Contraction theorem for generalized pairs
Lingyao Xie
TL;DR
This paper proves a contraction theorem for generalized pairs using Kollár's gluing theory, enabling the running of the minimal model program for generalized log canonical pairs.
Contribution
It introduces a contraction theorem for generalized pairs, expanding the tools available for the minimal model program in algebraic geometry.
Findings
Proves the contraction theorem for generalized pairs.
Enables running the MMP for generalized log canonical pairs.
Utilizes Kollár's gluing theory in the proof.
Abstract
We use Koll\'ar's gluing theory to prove the contraction theorem for generalized pairs. In particular, we show that we can run the MMP for any generalized log canonical pairs.
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Advanced Algebra and Logic · Logic, programming, and type systems