The Integral Closure of Ideals in ℂ{x, y}

Abstract

We give some techniques to determine the ideal K _I generated by the monomials x ^{k ₁} y ^{k ₂} belonging to the integral closure Ī of an ideal I ⊆ ℂ{x, y}. We also give a sufficient condition for a weighted homogeneous ideal I ⊆ ℂ{x, y} to satisfy the relation Ī = I + K _I .

Key Words:

• Integral closure of ideals
• Monomial ideals
• Newton polyhedra

2000 Mathematics Subject Classification:

• Primary 13A30
• Secondary 13B20

Acknowledgment

Work supported by DGICYT Grant BFM2000–1110.