The Hilbert series of the ring associated to an almost alternating matrix

TL;DR

This paper provides an explicit formula for the Hilbert Series of a specific algebra associated with a residual intersection of a grade three Gorenstein ideal, advancing understanding in algebraic geometry and commutative algebra.

Contribution

It introduces a new explicit formula for the Hilbert Series of algebras linked to almost alternating matrices, expanding computational tools in algebraic geometry.

Findings

Derived an explicit Hilbert Series formula for the algebra

Applied the formula to residual intersections of Gorenstein ideals

Enhanced computational methods in algebraic geometry

Abstract

We give an explicit formula for the Hilbert Series of an algebra defined by a linearly presented, standard graded, residual intersection of a grade three Gorenstein ideal.