Face rings of complexes with singularities
نویسنده
چکیده
It is shown that the face ring of a pure simplicial complex modulo m generic linear forms is a ring with finite local cohomology if and only if the link of every face of dimension m or more is nonsingular. 2000 Mathematics Subject Classification: 13F55.
منابع مشابه
Rings of Singularities
This paper is a slightly revised version of an introduction into singularity theory corresponding to a series of lectures given at the ``Advanced School and Conference on homological and geometrical methods in representation theory'' at the International Centre for Theoretical Physics (ICTP), Miramare - Trieste, Italy, 11-29 January 2010. We show how to associate to a triple of posit...
متن کاملFace rings of simplicial complexes with singularities
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 cohomolog...
متن کاملFace numbers of pseudomanifolds with isolated singularities
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 and upper bound theorems when the singularities are also homologically isolated. We give formulas for the Hilbert function of a generic...
متن کاملFace ring multiplicity via CM-connectivity sequences
The multiplicity conjecture of Herzog, Huneke, and Srinivasan is verified for the face rings of the following classes of simplicial complexes: matroid complexes, complexes of dimension one and two, and Gorenstein complexes of dimension at most four. The lower bound part of this conjecture is also established for the face rings of all doubly Cohen-Macaulay complexes whose 1-skeleton’s connectivi...
متن کاملGröbner Bases and Betti Numbers of Monoidal Complexes
Combinatorial commutative algebra is a branch of combinatorics, discrete geometry, and commutative algebra. On the one hand, problems from combinatorics or discrete geometry are studied using techniques from commutative algebra; on the other hand, questions in combinatorics motivated various results in commutative algebra. Since the fundamental papers of Stanley (see [13] for the results) and H...
متن کامل