A. Hardesty

collaborators

4 papers

math.AC2025

Realizing Algebra Structures on Free Resolutions of Grade 3 Perfect Ideals

Alexis Hardesty

Perfect ideals $I$ of grade $3$ in a local ring $(R, m, k)$ can be classified based on multiplicative structures on $Tor_{∙}^{R} (R / I, k)$ . The classifica…

math.AC2024

Sampling Algebra Structures on Minimal Free Resolutions

Lars Winther Christensen, Orin Gotchey, Alexis Hardesty

Ideals in the ring of power series in three variables can be classified based on algebra structures on their minimal free resolutions. The classification is incomplete in the sense…

math.AC2024

The Tor algebra of trimmings of Gorenstein ideals

Luigi Ferraro, Alexis Hardesty

Let $(R, m, k)$ be a regular local ring of dimension 3. Let $I$ be a Gorenstein ideal of $R$ of grade 3. Buchsbaum and Eisenbud proved that there is a skew-symmetric m…

math.RA2024

The Eliahou-Kervaire resolution over a skew polynomial ring

Luigi Ferraro, Alexis Hardesty

In a 1987 paper, Eliahou and Kervaire constructed a minimal resolution of a class of monomial ideals in a polynomial ring, called stable ideals. As a consequence of their construct…