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Log–canonical forms and log canonical singularities

Log-canonical forms and log canonical singularities

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jun 2003Embargo end date: 01 Jan 2000Publisher:WileyJournal:Mathematische Nachrichten, volume 254-255, pages 107-125 (issn: 0025-584X, eissn: 1522-2616,

Authors: Zaidenberg, Mikhail; Flenner, Hubert;

doi: 10.1002/mana.200310056 , 10.48550/arxiv.math/0012122

arXiv: http://arxiv.org/abs/math/0012122

Log–canonical forms and log canonical singularities

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Abstract

AbstractFor a normal subvarietyVof ℂnwith a good ℂ*–action we give a simple characterization for when it has only log canonical, log terminal or rational singularities. Moreover we are able to give formulas for the plurigenera of isolated singular points of such varieties and of the logarithmic Kodaira dimension ofV\{0}. For this purpose we introduce sheaves ofm–canonical andL2,m–canonical forms on normal complex spaces. For the case of affine varieties with good C*–action we give an explicit formula for these sheaves in terms of the grading of the dualizing sheaf and its tensor powers.

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Keywords

Global theory of complex singularities; cohomological properties, 14B05 (primary), 14J17 (secondary), [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], Kodaira dimension, Singularities in algebraic geometry, Complex surface and hypersurface singularities, Mathematics - Algebraic Geometry, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, graded algebra, FOS: Mathematics, quasihomogeneous singularity, Algebraic Geometry (math.AG)

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