Local cohomology of logarithmic forms

G. Denham[1]; H. Schenck[2]; M. Schulze[3]; M. Wakefield[4]; U. Walther[5]

  • [1] University of Western Ontario Department of Mathematics London, Ontario N6A 5B7 (Canada)
  • [2] University of Illinois Department of Mathematics Urbana, IL 61801 (USA)
  • [3] University of Kaiserslautern Department of Mathematics 67663 Kaiserslautern (Germany)
  • [4] United States Naval Academy Department of Mathematics Annapolis, MD 21402 (USA)
  • [5] Purdue University Department of Mathematics West Lafayette, IN 47907 (USA)

Annales de l’institut Fourier (2013)

  • Volume: 63, Issue: 3, page 1177-1203
  • ISSN: 0373-0956

Abstract

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Let Y be a divisor on a smooth algebraic variety X . We investigate the geometry of the Jacobian scheme of Y , homological invariants derived from logarithmic differential forms along Y , and their relationship with the property that Y be a free divisor. We consider arrangements of hyperplanes as a source of examples and counterexamples. In particular, we make a complete calculation of the local cohomology of logarithmic forms of generic hyperplane arrangements.

How to cite

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Denham, G., et al. "Local cohomology of logarithmic forms." Annales de l’institut Fourier 63.3 (2013): 1177-1203. <http://eudml.org/doc/275575>.

@article{Denham2013,
abstract = {Let $Y$ be a divisor on a smooth algebraic variety $X$. We investigate the geometry of the Jacobian scheme of $Y$, homological invariants derived from logarithmic differential forms along $Y$, and their relationship with the property that $Y$ be a free divisor. We consider arrangements of hyperplanes as a source of examples and counterexamples. In particular, we make a complete calculation of the local cohomology of logarithmic forms of generic hyperplane arrangements.},
affiliation = {University of Western Ontario Department of Mathematics London, Ontario N6A 5B7 (Canada); University of Illinois Department of Mathematics Urbana, IL 61801 (USA); University of Kaiserslautern Department of Mathematics 67663 Kaiserslautern (Germany); United States Naval Academy Department of Mathematics Annapolis, MD 21402 (USA); Purdue University Department of Mathematics West Lafayette, IN 47907 (USA)},
author = {Denham, G., Schenck, H., Schulze, M., Wakefield, M., Walther, U.},
journal = {Annales de l’institut Fourier},
keywords = {hyperplane arrangement; logarithmic; differential form; free divisor; logarithmic differential form},
language = {eng},
number = {3},
pages = {1177-1203},
publisher = {Association des Annales de l’institut Fourier},
title = {Local cohomology of logarithmic forms},
url = {http://eudml.org/doc/275575},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Denham, G.
AU - Schenck, H.
AU - Schulze, M.
AU - Wakefield, M.
AU - Walther, U.
TI - Local cohomology of logarithmic forms
JO - Annales de l’institut Fourier
PY - 2013
PB - Association des Annales de l’institut Fourier
VL - 63
IS - 3
SP - 1177
EP - 1203
AB - Let $Y$ be a divisor on a smooth algebraic variety $X$. We investigate the geometry of the Jacobian scheme of $Y$, homological invariants derived from logarithmic differential forms along $Y$, and their relationship with the property that $Y$ be a free divisor. We consider arrangements of hyperplanes as a source of examples and counterexamples. In particular, we make a complete calculation of the local cohomology of logarithmic forms of generic hyperplane arrangements.
LA - eng
KW - hyperplane arrangement; logarithmic; differential form; free divisor; logarithmic differential form
UR - http://eudml.org/doc/275575
ER -

References

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