Techniques for the Analytic Proof of the Finite Generation of the Canonical Ring

Abstract

This article is written for the Proceedings of the Conference on Current Developments in Mathematics in Harvard University, November 16-17, 2007. It is an exposition of the analytic proof of the finite generation of the canonical ring for a compact complex algebraic manifold of general type. It lists and discusses the main techniques and explains how they are put together in the proof. Of the various main techniques some special attention is given to (i) the technique of discrepancy subspaces and (ii) the technique of subspaces of minimum additional vanishing.

References in corpus (4)

• Existence of minimal models for varieties of log general type
• A General Non-Vanishing Theorem and an Analytic Proof of the Finite Generation of the Canonical Ring
• Relative critical exponents, non-vanishing and metrics with minimal singularities
• Additional Explanatory Notes on the Analytic Proof of the Finite Generation of the Canonical Ring

Cited by in corpus (1)

• Dynamic multiplier ideal sheaves and the construction of rational curves in Fano manifolds