Bases and Ideal Generators for Projective Monomial Curves

Abstract

In this article we study bases for projective monomial curves and the relationship between the basis and the set of generators for the defining ideal of the curve. We understand this relationship best for curves in ℙ³ and for curves defined by an arithmetic progression. We are able to prove that the latter are set theoretic complete intersections.

Key Words:

• Arithmetic progression
• Ideal generators
• Projective monomial curve
• Set-theoretic complete intersection
• Semigroup

2000 Mathematics Subject Classification:

• Primary 14H50
• 14M10
• 20M25

ACKNOWLEDGMENT

This work was done while the second author was visiting the Department of Mathematics and Statistics, Queens University, Kingston, Canada, and was partially supported by the NSERC grant of the third author. The second author thanks Department of Mathematics and Statistics, Queens University, Kingston, Canada, for its hospitality.

Notes

Communicated by R. Wiegand.