Complete intersections

Apostolos Thoma, Purdue University

Abstract

We give a necessary and sufficient condition for monomial curves in the three dimensional projective space to be a set theoretic complete intersections on a binomial surface. Using this condition, we prove that the twisted cubic curve is the only smooth monomial curve which is a set theoretic complete intersection on a binomial surface, in characteristic zero. We describe the monomial curves that are set theoretical complete intersections on two binomial surfaces. We prove they are exactly those that are ideal theoretic complete intersections. Using that we get explicitly all monomial curves that are ideal theoretic complete intersections and a minimal generating basis for their ideals. Finally we prove that smooth monomial curves of degree greater than three are not set theoretic complete intersections on bihomogeneous surfaces.

Degree

Ph.D.

Advisors

Moh, Purdue University.

Subject Area

Mathematics

COinS