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Partial normalizations of Coxeter arrangements and discriminants

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.
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Contributor : Michel Granger Connect in order to contact the contributor
Submitted on : Monday, January 30, 2012 - 12:05:29 PM
Last modification on : Wednesday, October 20, 2021 - 3:18:47 AM
Long-term archiving on: : Wednesday, December 14, 2016 - 2:01:50 AM


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  • HAL Id : hal-00619215, version 2



Michel Granger, David Mond, Mathias Schulze. Partial normalizations of Coxeter arrangements and discriminants. 2011. ⟨hal-00619215v2⟩



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