GENERIC INITIAL IDEALS AND FIBRE PRODUCTS

Abstract

We study the behavior of generic initial ideals with respect to fibre products. In our main result we determine the generic initial ideal of the fibre product with respect to the reverse lexicographic order. As an application we compute explicitly the generic initial ideal of a fibre product in a special case. We also prove that the fibre product of two graded ideals is componentwise linear if and only if both ideals have this property.