dc.contributor.author | Granger, Michel | |
dc.contributor.author | Mond, David | |
dc.contributor.author | Nieto-Reyes, Alicia | |
dc.contributor.author | Schulze, Mathias | |
dc.date.accessioned | 2018-08-15T12:44:18Z | |
dc.date.available | 2018-08-15T12:44:18Z | |
dc.date.issued | 2009 | |
dc.identifier | oksd_granger_linearfreedivis_2009 | |
dc.identifier.citation | Granger, M., Mond, D., Nieto-Reyes, A., & Schulze, M. (2009). Linear free divisors and the global logarithmic comparison theorem. Annales de l'Institut Fourier, 59(2), 811-850. https://doi.org/10.5802/aif.2448 | |
dc.identifier.uri | https://hdl.handle.net/11244/301406 | |
dc.description.abstract | A complex hypersurface D in C^n is a linear free divisor (LFD) if its module of logarithmic vector fields has a global basis of linear vector fields. We classify all LFDs for n at most 4. | |
dc.description.abstract | By analogy with Grothendieck's comparison theorem, we say that the global logarithmic comparison theorm (GLCT) holds for D if the complex of global logarithmic differential forms computes the complex cohomology of C^n \ D. We develop a general criterion for the GLCT for LFDs and prove that it is fulfilled whenever the Lie algebra of linear logarithmic vector fields is reductive. For n at most 4, we show that the GLCT holds for all LFDs. | |
dc.description.abstract | We show that LFDs arising naturally as discriminants in quiver representation spaces (of real Schur roots) fulfill the GLCT. As a by-product we obtain a topological proof of a theorem of V. Kac on the number of irreducible components of such discriminants. | |
dc.format | application/pdf | |
dc.language | en_US | |
dc.language | fr_FR | |
dc.publisher | Association des Annales de l'Institut Fourier | |
dc.rights | This material has been previously published. In the Oklahoma State University Library's institutional repository this version is made available through the open access principles and the terms of agreement/consent between the author(s) and the publisher. The permission policy on the use, reproduction or distribution of the material falls under fair use for educational, scholarship, and research purposes. Contact Digital Resources and Discovery Services at lib-dls@okstate.edu or 405-744-9161 for further information. | |
dc.title | Linear free divisors and the global logarithmic comparison theorem | |
osu.filename | oksd_granger_linearfreedivis_2009.pdf | |
dc.description.peerreview | Peer reviewed | |
dc.identifier.doi | 10.5802/aif.2448 | |
dc.description.department | Mathematics | |
dc.type.genre | Article | |
dc.type.material | Text | |
dc.subject.keywords | free divisor | |
dc.subject.keywords | prehomogeneous vector space | |
dc.subject.keywords | de rham cohomology | |
dc.subject.keywords | logarithmic comparison theorem | |
dc.subject.keywords | lie algebra cohomology | |
dc.subject.keywords | quiver representation | |