On the type and generators of monomial curves

Authors : Nguyen Thi DUNG

Pages : 2112-2124

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Let $n_1, n_2,\ldots, n_d$ be positive integers and $H $ be the numerical semigroup generated by $n_1,n_2, \ldots, n_d$. Let $A:=k[H]:=k[t^{n_1}, t^{n_2},\ldots, t^{n_d}]\cong k[x_1,x_2,\ldots,x_d]/I$ be the numerical semigroup ring of $H $ over $k.$ In this paper we give a condition $insert ignore into journalissuearticles values(*);$ that implies that the minimal number of generators of the defining ideal $I$ is bounded explicitly by its type. As a consequence for semigroups with $d=4$ satisfying the condition $insert ignore into journalissuearticles values(*);$ we have $\mu insert ignore into journalissuearticles values({\rm in}insert ignore into journalissuearticles values(I););\leq 2insert ignore into journalissuearticles values(tinsert ignore into journalissuearticles values(H););+1$.
Keywords : Frobenius number, pseudo Frobenius number, almost Gorenstein ring, semigroup rings, monomial curve