Logarithmic cohomology of the complement of a plane curve
FJ Calderón Moreno, D Mond… - Commentarii …, 2002 - Springer
Commentarii Mathematici Helvetici, 2002•Springer
Let D, x be a plane curve germ. We prove that the complex Ω^∙(\logD)_x computes the
cohomology of the complement of D, x only if D is quasihomogeneous. This is a partial
converse to a theorem of 5, which asserts that this complex does compute the cohomology
of the complement, whenever D is a locally weighted homogeneous free divisor (and so in
particular when D is a quasihomogeneous plane curve germ). We also give an example of a
free divisor D⊂C^3 which is not locally weighted homogeneous, but for which this (second) …
cohomology of the complement of D, x only if D is quasihomogeneous. This is a partial
converse to a theorem of 5, which asserts that this complex does compute the cohomology
of the complement, whenever D is a locally weighted homogeneous free divisor (and so in
particular when D is a quasihomogeneous plane curve germ). We also give an example of a
free divisor D⊂C^3 which is not locally weighted homogeneous, but for which this (second) …
Abstract
Let D, x be a plane curve germ. We prove that the complex computes the cohomology of the complement of D, x only if D is quasihomogeneous. This is a partial converse to a theorem of [5], which asserts that this complex does compute the cohomology of the complement, whenever D is a locally weighted homogeneous free divisor (and so in particular when D is a quasihomogeneous plane curve germ). We also give an example of a free divisor which is not locally weighted homogeneous, but for which this (second) assertion continues to hold.
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