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.

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Cited by in corpus (49)

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• A variational approach to complex Monge-Ampere equations
• Birational geometry for number theorists
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• On Log Canonical Models of the Moduli Space of Stable Pointed Curves
• A new geometric approach to problems in birational geometry
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• Anticanonical system of Fano fivefolds
• Canonical singular hermitian metrics on relative logcanonical bundles
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• Birational geometry of rational quartic surfaces
• Effective Iitaka fibrations
• Ricci iterations and canonical Kähler-Einstein currents on log canonical pairs
• Towards Mori's program for the moduli space of stable maps
• Minimal models, flips and finite generation : a tribute to V.V. SHOKUROV and Y.-T. SIU
• Extension of sections via adjoint ideals
• Varieties with generically nef tangent bundles
• Compactifications of smooth families and of moduli spaces of polarized manifolds
• Notes on the log minimal model program
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• On Effective log Iitaka Fibration for 3-folds and 4-folds
• Flops connect minimal models
• Equivalent Birational Embeddings III: cones
• On pluricanonical systems of algebraic varieties of general type
• $L^2$ extension of adjoint line bundle sections
• Picard-graded Betti numbers and the defining ideals of Cox rings
• Variations on Log Sarkisov Program for Surfaces
• Techniques for the Analytic Proof of the Finite Generation of the Canonical Ring
• Convex bodies appearing as Okounkov bodies of divisors
• On Shokurov-type b-divisorial algebras of higher rank
• Arakelov (in)equalities
• Two local inequalities
• Moving and ample cones of holomorphic symplectic fourfolds
• Canonical measures and Kahler-Ricci flow
• Log minimal models according to Shokurov
• Fano manifolds obtained by blowing up along curves with maximal Picard number
• Degenerations of Rationally Connected Varieties
• A note on the projective varieties of almost general type
• A Lefschetz hyperplane theorem for Mori dream spaces
• Hilbert scheme of a pair of codimension two linear subspaces
• On existence of log minimal models and weak Zariski decompositions
• On Fano manifolds with a birational contraction sending a divisor to a curve
• A survey on Cox rings