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Claudia Miller

  1. Duality for Koszul Homology over Gorenstein Rings.

    Чт, 12/15/2011 - 15:01 — SomNambul
    Authors: Claudia Miller, Hamidreza Rahmati, Janet Striuli
    Subjects: Commutative Algebra
    Abstract

    We study Koszul homology over Gorenstein rings. If an ideal is strongly
    Cohen-Macaulay, the Koszul homology algebra satisfies Poincar\'e duality. We
    prove a version of this duality which holds for all ideals and allows us to
    give two criteria for an ideal to be strongly Cohen-Macaulay. The first can be
    compared to a result of Hartshorne and Ogus; the second is a generalization of
    a result of Herzog, Simis, and Vasconcelos using sliding depth.

  2. A Direct Limit for Limit Hilbert-Kunz Multiplicity for Smooth Projective Curves.

    Пт, 04/15/2011 - 15:01 — SomNambul
    Authors: Holger Brenner, Jinjia Li, Claudia Miller
    Subjects: Commutative Algebra
    Abstract

    This paper concerns the question of whether a more direct limit can be used
    to obtain the limit Hilbert Kunz multiplicity, a possible candidate for a
    characteristic zero Hilbert-Kunz multiplicity. The main goal is to establish an
    affirmative answer for one of the main cases for which the limit Hilbert Kunz
    multiplicity is even known to exist, namely that of graded ideals in the
    homogeneous coordinate ring of smooth projective curves.

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