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Mosc. Math. J., 2012, Volume 12, Number 2, Pages 335–367 (Mi mmj470)  

This article is cited in 1 scientific paper (total in 1 paper)

Partial normalizations of Coxeter arrangements and discriminants

Michel Grangera, David Mondb, Mathias Schulzec

a Université d'Angers, Département de Mathématiques, LAREMA, CNRS UMR no 6093, 2 Bd Lavoisier, 49045 Angers, France
b Mathematics Institute, University of Warwick, Coventry CV47AL, England
c Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, United States

Abstract: We study natural partial normalization spaces of Coxeter arrangements and discriminants and relate their geometry to representation theory. The underlying ring structures arise from Dubrovin's Frobenius manifold structure which is lifted (without unit) to the space of the arrangement. We also describe an independent approach to these structures via duality of maximal Cohen–Macaulay fractional ideals. In the process, we find 3rd order differential relations for the basic invariants of the Coxeter group. Finally, we show that our partial normalizations give rise to new free divisors.

Key words and phrases: Coxeter group, logarithmic vector field, free divisor.

DOI: https://doi.org/10.17323/1609-4514-2012-12-2-335-367

Full text: http://www.ams.org/.../abst12-2-2012.html
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Bibliographic databases:

MSC: 20F55, 17B66, 13B22
Received: September 1, 2011; in revised form January 20, 2012
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Citation: Michel Granger, David Mond, Mathias Schulze, “Partial normalizations of Coxeter arrangements and discriminants”, Mosc. Math. J., 12:2 (2012), 335–367

Citation in format AMSBIB
\Bibitem{GraMonSch12}
\by Michel~Granger, David~Mond, Mathias~Schulze
\paper Partial normalizations of Coxeter arrangements and discriminants
\jour Mosc. Math.~J.
\yr 2012
\vol 12
\issue 2
\pages 335--367
\mathnet{http://mi.mathnet.ru/mmj470}
\crossref{https://doi.org/10.17323/1609-4514-2012-12-2-335-367}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2978760}
\zmath{https://zbmath.org/?q=an:06126177}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000309365900008}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Boehm J., Decker W., Schulze M., “Local Analysis of Grauert-Remmert-Type Normalization Algorithms”, Int. J. Algebr. Comput., 24:1 (2014), 69–94  crossref  mathscinet  isi  scopus
  • Moscow Mathematical Journal
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