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

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arxiv 0811.1211 v1 pith:LWXNRYAY submitted 2008-11-07 math.AG math.CVmath.DG

Yum-Tong Siu This is my paper · ORCID
classification math.AGmath.CVmath.DG
keywords prooftechniquesanalyticcanonicalfinitegenerationmainring
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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.

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  1. H\"older estimates for degenerate complex Monge-Amp\`ere equations

    math.CV 2025-08 conditional novelty 8.0 of 10

    Hölder estimates for degenerate complex Monge-Ampère equations are established on smoothable singular Kähler varieties, confirming a conjecture for Kähler-Einstein potentials.

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