ON THE NORMALITY OF MONOMIAL IDEALS OF MIXED PRODUCTS

Abstract

Let R = K[x, y] be a polynomial ring in two disjoint sets of variables x, y over a field K. We study ideals of mixed products L = I_kJ_r + I_sJ_t such that k + r = s + t, where I_k (resp. J_r ) denotes the ideal of R generated by the square-free monomials of degree k (resp. r) in the x (resp. y ) variables. Our main result is a characterization of when a given ideal L of mixed products is normal.

^*Partially supported by CONACyT grant 27931E and SNI, México.

ACKNOWLEDGMENT

This paper was written when the second author was visiting the University of Messina with the support of the Istituto Nazionale Di Alta Matematica Francesco Severi; he thanks both institutions for making this visit possible and for their hospitality.

Notes

^*Partially supported by CONACyT grant 27931E and SNI, México.