Vanishing theorems for generalized pairs

Bingyi Chen; Jihao Liu; Lingyao Xie

Vanishing theorems for generalized pairs

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arxiv 2305.12337 v1 pith:QE4ONQSH submitted 2023-05-21 math.AG

Bingyi Chen , Jihao Liu , Lingyao Xie This is my paper · ORCID

classification math.AG

keywords generalizedpairstheoremvanishingallowsapproachbase-point-freenessconsequence

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We establish the Kodaira vanishing theorem and the Kawamata-Viehweg vanishing theorem for lc generalized pairs. As a consequence, we provide a new proof of the base-point-freeness theorem for lc generalized pairs. This new approach allows us to prove the contraction theorem for lc generalized pairs without using Koll\'ar's gluing theory.

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$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs
math.AG 2025-01 conditional novelty 7.0 of 10

A P-trivial MMP is introduced and used to show that several classes of generalised klt and lc pairs with Nakayama-Zariski decompositions have minimal models.

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