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Adam S. Sikora

  1. Algebraic description of character varieties.

    Mon, 06/27/2011 - 15:01 — SomNambul
    Authors: Adam S. Sikora
    Subjects: Algebraic Geometry
    Abstract

    We find finite, reasonably small, generator sets of the coordinate rings of
    G-character varieties of finitely generated groups for all classical groups G.
    This result together with the method of Grobner basis gives an algorithm for
    describing character varieties by explicit polynomial equations.

  2. Character Varieties.

    Tue, 08/25/2009 - 22:41 — SomNambul
    Authors: Adam S. Sikora
    Subjects: Representation Theory
    Abstract

    Let G be a complex reductive algebraic group and let Gamma be a finitely
    generated group. We study irreducible and completely reducible representations
    rho: Gamma -> G in the context of the geometric invariant theory of the
    G-action on Hom(Gamma,G) by conjugation.

    Additionally, we study properties of character varieties, Hom(Gamma,G)//G. In
    particular we describe the tangent spaces to X_G(Gamma) in terms of first
    cohomology groups of Gamma with twisted coefficients, generalizing the well
    known formula.

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