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BETTI NUMBERS FOR CERTAIN COHEN–MACAULAY TANGENT CONES

Part of: Curves Local rings and semilocal rings Computational aspects and applications

Published online by Cambridge University Press:  30 August 2018

MESUT ŞAHİN Open the ORCID record for MESUT ŞAHİN [Opens in a new window]  and
NİL ŞAHİN
MESUT ŞAHİN*
Affiliation:
Department of Mathematics, Hacettepe University, Beytepe, 06800, Ankara, Turkey email [email protected]
NİL ŞAHİN
Affiliation:
Department of Industrial Engineering, Bilkent University, Ankara, 06800, Turkey email [email protected]
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

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We compute Betti numbers for a Cohen–Macaulay tangent cone of a monomial curve in the affine $4$-space corresponding to a pseudo-symmetric numerical semigroup. As a byproduct, we also show that for these semigroups, being of homogeneous type and homogeneous are equivalent properties.

Keywords

numerical semigroup ringsmonomial curvestangent conesBetti numbersfree resolutions

MSC classification

Primary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
Secondary: 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 14H20: Singularities, local rings
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 99 , Issue 1 , February 2019 , pp. 68 - 77
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

The authors were supported by the project 114F094 under the program 1001 of the Scientific and Technological Research Council of Turkey.

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