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.
Vanishing theorems for generalized pairs
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abstract
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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2025 1verdicts
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$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs
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.