BLOW-UP OF STRAIGHTENING-CLOSED IDEALS IN ORDINAL HODGE ALGEBRAS

Abstract

We study a class of ideals I in graded ordinal Hodge algebras A. These ideals are distinguished by the fact that their powers have a canonical standard basis. This leads to Hodge algebra structures on the Rees ring and the associated graded ring. Furthermore, from a natural standard filtration one obtains a depth bound for A/I(n) which, under certain conditions, is sharp for n large. Frequently one observes that I(n) = I(n). Under suitable hypotheses it is possible to calculate the divisor class group of the Rees algebra. Our main examples are ideals of ``virtual'' maximal minors and ideals of maximal minors ``fixing a submatrix''.