Existence of minimal models for varieties of log general type

Abstract

We prove that the canonical ring of a smooth projective variety is finitely generated.

References in corpus (1)

• A General Non-Vanishing Theorem and an Analytic Proof of the Finite Generation of the Canonical Ring

Cited by in corpus (29)

• The Kahler-Ricci flow through singularities
• Log minimal model program for the moduli space of stable curves: The first flip
• Log canonical thresholds of smooth Fano threefolds. With an appendix by Jean-Pierre Demailly
• A variational approach to complex Monge-Ampere equations
• Birational geometry for number theorists
• Dynamic multiplier ideal sheaves and the construction of rational curves in Fano manifolds
• On Log Canonical Models of the Moduli Space of Stable Pointed Curves
• Minimal models, flips and finite generation : a tribute to V.V. SHOKUROV and Y.-T. SIU
• Towards Mori's program for the moduli space of stable maps
• Varieties with generically nef tangent bundles
• Notes on the log minimal model program
• Iitaka conjecture $C_{n,m}$ in dimension six
• On Effective log Iitaka Fibration for 3-folds and 4-folds
• Flops connect minimal models
• Picard-graded Betti numbers and the defining ideals of Cox rings
• $L^2$ extension of adjoint line bundle sections
• On pluricanonical systems of algebraic varieties of general type
• Variations on Log Sarkisov Program for Surfaces
• Techniques for the Analytic Proof of the Finite Generation of the Canonical Ring
• Log minimal models according to Shokurov
• Canonical measures and Kahler-Ricci flow
• Arakelov (in)equalities
• On Shokurov-type b-divisorial algebras of higher rank
• Moving and ample cones of holomorphic symplectic fourfolds
• On Fano manifolds with a birational contraction sending a divisor to a curve
• On existence of log minimal models and weak Zariski decompositions
• Fano manifolds obtained by blowing up along curves with maximal Picard number
• A survey on Cox rings
• Hilbert scheme of a pair of codimension two linear subspaces