Vanishing Ideals Over Odd Cycles

Abstract

Let K be a finite field. Let X* be a subset of the a ne space Kn, which is parameterized by odd cycles. In this paper we give an explicit Gröbner basis for the vanishing ideal, I(X*), of X*. We give an explicit formula for the regularity of I(X*) and finally if X* is parameterized by an odd cycle of length k, we show that the Hilbert function of the vanishing ideal of X* can be written as linear combination of Hilbert functions of degenerate torus.

Keywords

• toric set
• parameterized code
• hilbert function
• vanishing ideal
• regularity index
• primary 13p25
• secondary 14g50, 14g15, 11t71, 94b27, 94b05