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Article overview
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Cohen-Macaulay semi-log canonical singularities are Du Bois | Sándor J. Kovács
; Karl E. Schwede
; Karen E. Smith
; | Date: |
10 Jan 2008 | Abstract: | We prove that a Cohen-Macaulay normal variety $X$ has Du Bois singularities
if and only if $pi_*omega_{X’}(G) simeq omega_X$ for a log resolution $pi:
X’ o X$, where $G$ is the reduced exceptional divisor of $pi$. Many basic
theorems about Du Bois singularities become transparent using this
characterization. We also prove Koll’ar’s conjecture that semi-log-canonical
singularities are Du Bois, in the Cohen-Macaulay case. It also follows that the
Kodaira vanishing theorem holds for semi log canonical varieties and that
Cohen-Macaulay semi-log-canonical singularities are cohomologically
insignificant in the sense of Dolgachev. | Source: | arXiv, 0801.1541 | Services: | Forum | Review | PDF | Favorites |
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