In this work, we calculate the regularity and a-invariant of blowup algebras derived from modules that are direct sums of two-sided ladder determinantal ideals. We establish necessary and sufficient conditions for these blowup algebras to exhibit the Gorenstein property, and we provide both upper and lower bounds for their multiplicity. Furthermore, our results allow us to determine the reduction numbers of the modules within this class.

This is joint work with Alessandra Costantini, Louiza Fouli, Kriti Goel, Kuei-Nuan Lin, Haydee Lindo, and Whitney Liske.