Betti sequence of the projective closure of affine monomial curves

Authors

Joydip Saha, Indian Statistical Institute, Kolkata
Indranath Sengupta, Indian Institute of Technology Gandhinagar
Pranjal Srivastava, Indian Institute of Technology Gandhinagar

Article Type

Research Article

Publication Title

Journal of Symbolic Computation

Abstract

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.

First Page

101

Last Page

111

DOI

https://10.1016/j.jsc.2023.02.009

Publication Date

11-1-2023

Recommended Citation

Saha, Joydip; Sengupta, Indranath; and Srivastava, Pranjal, "Betti sequence of the projective closure of affine monomial curves" (2023). Journal Articles. 3528.
https://digitalcommons.isical.ac.in/journal-articles/3528