A valuative approach to the anticanonical minimal model program

2025/06/16 by Sung Rak Choi, Choi, Sung Rak, Sungwook Jang +5 · 1 citation
Engineering · #Advanced Numerical Methods in Computational Mathematics #Nuclear reactor physics and engineering

paper · pdf · doi:10.48550/arxiv.2506.13637

Abstract

In this paper, we show that the log canonical threshold of a potentially klt triple can be computed by a quasi-monomial valuation. The notion of potential triples provides a larger and more flexible framework to work with than that of generalized pairs. Our main result can be considered as an extension to the result of Xu on klt pairs. As an application of the main result, we show that we can run the MMP on any potentially klt triples and -(K_X+Δ)-MMP on the potentially klt pairs.

Citations

• On minimal model program and Zariski decomposition of potential triples
• Anticanonical minimal models and Zariski decomposition
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• Generalised pairs in birational geometry
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• Anti-pluricanonical systems on Fano varieties
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• A refinement of Izumi's Theorem
• Algebraic bounds on analytic multiplier ideals
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• Valuations and asymptotic invariants for sequences of ideals
• Existence of minimal models for varieties of log general type
• A derived category approach to generic vanishing

Cited by

• Asymptotically flat divisors and strongly F-regular type varieties

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• A Minimizing Valuation is Quasi-monomial
• Remarks on the existence of minimal models of log canonical generalized pairs
• Log Canonical Minimal Model Program for corank one foliations on Threefolds