Implementing the Kustin-Miller complex construction
Janko Boehm, Stavros Argyrios Papadakis
TL;DR
This paper details the implementation of the Kustin-Miller complex construction in Macaulay2, enabling the creation and analysis of high-codimension Gorenstein rings through explicit examples.
Contribution
It introduces a computational implementation of the Kustin-Miller complex in Macaulay2, facilitating practical applications in algebraic geometry.
Findings
Implementation in Macaulay2 available for use.
Demonstrated application on explicit examples.
Enhanced understanding of Gorenstein rings of high codimension.
Abstract
The Kustin-Miller complex construction, due to A. Kustin and M. Miller, can be applied to a pair of resolutions of Gorenstein rings with certain properties to obtain a new Gorenstein ring and a resolution of it. It gives a tool to construct and analyze Gorenstein rings of high codimension. We describe the Kustin-Miller complex and its implementation in the Macaulay2 package KustinMiller, and explain how it can be applied to explicit examples.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Commutative Algebra and Its Applications · Algebraic Geometry and Number Theory