Betti sequence of the projective closure of affine monomial curves

We introduce the notion of star gluing of numerical semigroups and show that this preserves the arithmetically Cohen-Macaulay and Gorenstein properties of the projective closure. Next, we give a sufficient condition involving Gröbner basis for the matching of Betti sequences of the affine curve and...

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Bibliographic Details
Published in:Journal of symbolic computation 2023-11, Vol.119, p.101-111
Main Authors: Saha, Joydip, Sengupta, Indranath, Srivastava, Pranjal
Format: Article
Language:English
Subjects:
Betti numbers
Gröbner bases
Monomial curves
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Summary:We introduce the notion of star gluing of numerical semigroups and show that this preserves the arithmetically Cohen-Macaulay and Gorenstein properties of the projective closure. Next, we give a sufficient condition involving Gröbner basis for the matching of Betti sequences of the affine curve and its projective closure. We also study the effect of simple gluing on Betti sequences of the projective closure. Finally, we construct numerical semigroups by gluing, such that for every positive integer n, the last Betti number of the corresponding affine curve and its projective closure are both n.
ISSN:0747-7171
1095-855X
DOI:10.1016/j.jsc.2023.02.009