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LIFTINGS OF A MONOMIAL CURVE

Part of: General commutative ring theory Commutative algebra: Homological methods Computational aspects and applications Rings and algebras arising under various constructions Theory of modules and ideals

Published online by Cambridge University Press:  05 July 2018

MESUT ŞAHİN Open the ORCID record for MESUT ŞAHİN [Opens in a new window]
MESUT ŞAHİN*
Affiliation:
Department of Mathematics, Hacettepe University, Beytepe, 06800, Ankara, Turkey email [email protected]
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Abstract

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We study an operation, that we call lifting, creating nonisomorphic monomial curves from a single monomial curve. Our main result says that all but finitely many liftings of a monomial curve have Cohen–Macaulay tangent cones even if the tangent cone of the original curve is not Cohen–Macaulay. This implies that the Betti sequence of the tangent cone is eventually constant under this operation. Moreover, all liftings have Cohen–Macaulay tangent cones when the original monomial curve has a Cohen–Macaulay tangent cone. In this case, all the Betti sequences are just the Betti sequence of the original curve.

Keywords

numerical semigroup ringsmonomial curvestangent conesBetti numbers

MSC classification

Primary: 13A30: Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
Secondary: 13C13: Other special types 13D02: Syzygies, resolutions, complexes 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 16S36: Ordinary and skew polynomial rings and semigroup rings
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 2 , October 2018 , pp. 230 - 238
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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