Главная

Isabella Novik

  1. Face numbers of pseudomanifolds with isolated singularities.

    Чт, 04/29/2010 - 15:01 — SomNambul
    Authors: Isabella Novik, Ed Swartz
    Subjects: Combinatorics
    Abstract

    We investigate the face numbers of simplicial complexes with Buchsbaum vertex
    links, especially pseudomanifolds with isolated singularities. This includes
    deriving Dehn-Sommerville relations for pseudomanifolds with isolated
    singularities and establishing lower bound theorems when the singularities are
    also homologically isolated. We give formulas for the Hilbert function of a
    generic Artinian reduction of the face ring when the singularities are
    homologically isolated and for any pure two-dimensional complex.

  2. Face rings of simplicial complexes with singularities.

    Втр, 01/19/2010 - 16:01 — SomNambul
    Authors: Ezra Miller, Isabella Novik, Ed Swartz
    Subjects: Commutative Algebra
    Abstract

    The face ring of a simplicial complex modulo m generic linear forms is shown
    to have finite local cohomology if and only if the link of every face of
    dimension m or more is `nonsingular', i.e., has the homology of a wedge of
    spheres of the expected dimension. This is derived from an enumerative result
    for local cohomology of face rings modulo generic linear forms, as compared
    with local cohomology of the face ring itself. The enumerative result is
    generalized in slightly weaker form to squarefree modules.

  3. Face numbers of generalized balanced Cohen-Macaulay complexes.

    Втр, 09/08/2009 - 12:16 — SomNambul
    Authors: Jonathan Browder, Isabella Novik
    Subjects: Combinatorics
    Abstract

    A common generalization of two theorems on the face numbers of Cohen-Macaulay
    (CM, for short) simplicial complexes is established: the first is the theorem
    of Stanley (necessity) and Bjorner-Frankl-Stanley (sufficiency) that
    characterizes all possible face numbers of a-balanced CM complexes, while the
    second is the theorem of Novik (necessity) and Browder (sufficiency) that
    characterizes the face numbers of CM subcomplexes of the join of the boundaries
    of simplices.

Math-arch

RSS-материал