Computing The Invariants Of Intersection Algebras Of Principal Monomial Ideals

We continue the study of intersection algebras B = B-R(I, J) of two ideals I, J in a commutative Noetherian ring R. In particular, we exploit the semigroup ring and toric structures in order to calculate various invariants of the intersection algebra when R is a polynomial ring over a field and I, J are principal monomial ideals. Specifically, we calculate the F-signature, divisor class group, and Hilbert-Samuel and Hilbert-Kunz multiplicities, sometimes restricting to certain cases in order to obtain explicit formulae. This provides a new class of rings where formulae for the F-signature and Hilbert Kunz multiplicity, dependent on families of parameters, are provided.