New outlook on the Minimal Model Program, II

Abstract

We prove that the finite generation of adjoint rings proved in [Cascini and Lazić] implies all the foundational results of the Minimal Model Program: the Rationality, Cone and Contraction theorems, the existence of flips, and termination of flips with scaling in the presence of a big boundary.

to appear in Math. Ann

References in corpus (3)

• New outlook on the Minimal Model Program, I
• Relative critical exponents, non-vanishing and metrics with minimal singularities
• The Minimal Model Program Revisited

Cited by in corpus (9)

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• Finite generation and geography of models
• Abundance for varieties with many differential forms
• A note on the abundance conjecture
• On the number of minimal models of a log smooth threefold
• Small bandwidth ${\mathbb{C}}^{\ast }$-actions and birational geometry
• On the $4$-dimensional minimal model program for Kähler varieties
• Around and beyond the canonical class
• Programming the Minimal Model Program: a proposal