Asymptotic properties in the shifted family of a numerical semigroup with few generators

作者：Stamate Dumitru I^*

来源：Semigroup Forum, 2016, 93(2): 225-246.

DOI：10.1007/s00233-015-9724-2

• Numerical semigroup ring
• Tangent cone
• Periodicity
• Equations
• Complete intersection
• Betti numbers

Let be positive integers and for any integer consider the semigroup . If is any field, we study the defining relations of the semigroup ring and its tangent cone , for . Recent results in Herzog and Stamate (J Algebra 418:8-28, 2014), Jayanthan and Srinivasan (Proc Am Math Soc 141(12):4199-4208, 2013), and Vu (J Algebra 418:66-90, 2014), show that their Betti numbers are eventually periodic in . We give a better threshold than the one already known for which this happens and we describe how the defining equations are periodically changing. We explicitly find all the shifts that produce complete intersections, completing a result in Jayanthan and Srinivasan (2013). We write the minimal free resolution of and we show that its regularity is a quasilinear function for .

• 出版日期2016-10