Premium
Log–canonical forms and log canonical singularities
Author(s) -
Flenner Hubert,
Zaidenberg Mikhail
Publication year - 2003
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310056
Subject(s) - mathematics , kodaira dimension , subvariety , pure mathematics , gravitational singularity , sheaf , logarithm , coherent sheaf , affine transformation , mathematical analysis , variety (cybernetics) , statistics
For a normal subvariety V of ℂ n with 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 of V \{0}. For this purpose we introduce sheaves of m –canonical and L 2, 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.