Blowup algebras of determinantal modules

We study the blowup algebras of the modules that are direct sums of ideals generated by either maximal minors of a ladder matrix or unit interval determinantal ideals. Specifically, we determine Gröbner bases for the presentation ideals of multi-Rees algebras and their special fiber rings. Our analysis reveals that the multi-blowup algebras are Koszul Cohen–Macaulay normal domains, possess rational singularities in characteristic zero, and are F-rational in positive characteristic.