New outlook on the Minimal Model Program, I

Abstract

We give a new and self-contained proof of the finite generation of adjoint rings with big boundaries. As a consequence, we show that the canonical ring of a smooth projective variety is finitely generated.

to appear in Duke Math. J

References in corpus (3)

• New outlook on the Minimal Model Program, II
• The Minimal Model Program Revisited
• Existence of log canonical closures

Cited by in corpus (19)

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• Lagrangian fibrations on hyperkähler manifolds - On a question of Beauville
• Abundance for varieties with many differential forms
• New outlook on the Minimal Model Program, II
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• Extension theorems, Non-vanishing and the existence of good minimal models
• A note on the abundance conjecture
• On the number of minimal models of a log smooth threefold
• The Minimal Model Program Revisited
• Invariance of certain plurigenera for surfaces in mixed characteristics
• Small bandwidth ${\mathbb{C}}^{\ast }$-actions and birational geometry
• On the $4$-dimensional minimal model program for Kähler varieties
• Log canonical pairs with boundaries containing ample divisors
• On images of Mori dream spaces
• Around and beyond the canonical class
• Effective finite generation for adjoint rings
• Programming the Minimal Model Program: a proposal
• On the body of ample angles of asymptotically log Fano varieties
• Skoda division of line bundle sections and pseudo-division