Certain Minimal Varieties Are Set-Theoretic Complete Intersections

Abstract

We present a class of homogeneous ideals which are generated by monomials and binomials of degree 2 and are set-theoretic complete intersections. This class includes certain reducible varieties of minimal degree and, in particular, the presentation ideals of the fiber cone algebras of monomial varieties of codimension 2.

Key Words:

• Fiber cone
• Minimal variety
• Rational normal scroll
• Set-theoretic complete intersection

Mathematics Subject Classification (2000):

• 14M10
• 14M20

ACKNOWLEDGMENT

This article is partially supported by the Italian Ministry of Education, University and Research.

Notes

Communicated by R. H. Villarreal.