Hilbert functions of Gorenstein monomial curves

Download

index.pdf

Date

2007-01-01

Author

Arslan, Feza
Mete, Pinar

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

189
views

0
downloads

It is a conjecture due to M. E. Rossi that the Hilbert function of a one-dimensional Gorenstein local ring is non-decreasing. In this article, we show that the Hilbert function is non-decreasing for local Gorenstein rings with embedding dimension four associated to monomial curves, under some arithmetic assumptions on the generators of their de. ning ideals in the non-complete intersection case. In order to obtain this result, we determine the generators of their tangent cones explicitly by using standard basis computations under these arithmetic assumptions and show that the tangent cones are Cohen-Macaulay. In the complete intersection case, by characterizing certain families of complete intersection numerical semigroups, we give an inductive method to obtain large families of complete intersection local rings with arbitrary embedding dimension having non- decreasing Hilbert functions.

Subject Keywords

Applied Mathematics, General Mathematics

URI

https://hdl.handle.net/11511/65742

Journal

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

DOI

https://doi.org/10.1090/s0002-9939-07-08793-x

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Legendrian realization in convex Lefschetz fibrations and convex stabilizations Akbulut, Selman; Arıkan, Mehmet Fırat (Walter de Gruyter GmbH, 2015-05-01) We show that, up to a Liouville homotopy and a deformation of compact convex Lefschetz fibrations on W, any Lagrangian submanifold with trivial first de Rham cohomology group, embedded on a (symplectic) page of the (induced) convex open book on partial derivative W, can be assumed to be Legendrian in partial derivative W with the induced contact structure. This can be thought as the extension of Giroux's Legendrian realization (which holds for contact open books) for the case of convex open books. We also s...
Concrete description of CD0(K)-spaces as C(X)-spaces and its applications Ercan, Z (American Mathematical Society (AMS), 2004-01-01) We prove that for a compact Hausdorff space K without isolated points, CD0(K) and C(K x {0, 1}) are isometrically Riesz isomorphic spaces under a certain topology on K x {0, 1}. Moreover, K is a closed subspace of K x {0, 1}. This provides concrete examples of compact Hausdorff spaces X such that the Dedekind completion of C(X) is B(S) (= the set of all bounded real-valued functions on S) since the Dedekind completion of CD0(K) is B(K) (CD0(K, E) and CDw (K, E) spaces as Banach lattices).
On homology of real algebraic varieties Ozan, Yıldıray (American Mathematical Society (AMS), 2001-01-01) Let R be a commutative ring with unity and X an R-oriented compact nonsingular real algebraic variety of dimension n. If i : X --> X-C is any nonsingular complexification of X, then the kernel, which we will denote by KHk(X, R), of the induced homomorphism i(*) : H-k(X, R) --> H-k(X-C, R) is independent of the complexification. In this work, we study KHk(X, R) and give some of its applications.
Holomorphic extension of meromorphic mappings along real analytic hypersurfaces Yazıcı, Özcan (Springer Science and Business Media LLC, 2020-08-01) Let M subset of C-n be a real analytic hypersurface, M' subset of C-N (N >= n) be a strongly pseudoconvex real algebraic hypersurface of the special form, and F be a meromorphic mapping in a neighborhood of a point p is an element of M which is holomorphic in one side of M. Assuming some additional conditions for the mapping F on the hypersurface M, we proved that F has a holomorphic extension to p. This result may be used to show the regularity of CR mappings between real hypersurfaces of different dimensi...
Invariant subspaces for Banach space operators with an annular spectral set Yavuz, Onur (2008-01-01) Consider an annulus Omega = {z epsilon C : r(0) 0 such that parallel to p(T)parallel to <= K sup{vertical bar p(lambda)vertical bar : vertical bar lambda vertical bar <= 1} and parallel to p(r(0)T(-1))parallel to <= K sup{vertical bar p(lambda)vertical bar : vertical bar lambda vertical bar <= 1} for all polynomials p. Then there exists a nontrivial common invariant subspace for T* and T*(-1).

Citation Formats

F. Arslan and P. Mete, “Hilbert functions of Gorenstein monomial curves,” PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, pp. 1993–2002, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65742.