Projective Closure of Affine Monomial Curves II

Autor:	Saha, Joydip, Sengupta, Indranath, Srivastava, Pranjal
Rok vydání:	2021
Předmět:	Mathematics - Commutative Algebra 13D02 13F055 13P10 13P20
Druh dokumentu:	Working Paper
Popis:	In this paper our aim is twofold. First, we introduce the notion of star gluing of numerical semigroups and show that arithmetically Cohen-Macaulay and Gorenstein properties of the projective closure are preserved under this gluing operation. We then give a condition on Gr\"{o}bner basis of the defining ideal of an affine monomial curve which ensures that the Betti sequence of the affine curve is the same as the Betti sequence of its projective closure. We also study the effect of simple gluing on Betti sequences of the projective closure. Finally, we construct some numerical semigroups, using a gluing technique, such that the Cohen-Macaulay type of corresponding affine curve and its projective closure are both $n$. Comment: 23 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2111.13022 Zobrazit plný text záznamu View this record from Arxiv