BooksirmaCollected Volumepp. 59–84

Multiplicity of critical points of master functions and Schubert calculus

  • Prakash Belkale

    University of North Carolina at Chapel Hill, USA

  • Evgeny Mukhin

    Indiana University Purdue University Indianapolis, USA

  • Alexander Varchenko

    University of North Carolina at Chapel Hill, United States
Multiplicity of critical points of master functions and Schubert calculus cover

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Abstract

In [MV], some correspondences were defined between critical points of master functions associated to slN + 1 and subspaces of ℂ[x] with given ramification properties. In this paper we show that these correspondences are in fact scheme theoretic isomorphisms of appropriate schemes. This gives relations between multiplicities of critical point loci of the relevant master functions and multiplicities in Schubert calculus.