How to calculate A-Hilb C^3
Alastair Craw, Miles Reid
TL;DR
This paper presents a simplified method for calculating the A-Hilb C^3 for finite Abelian subgroups of SL(3,C), using continued fractions and tessellations, improving upon Nakamura's original algorithm.
Contribution
It introduces a more straightforward approach to compute A-Hilb C^3, avoiding complex algorithms by leveraging geometric and number-theoretic techniques.
Findings
Simplified calculation method for A-Hilb C^3
Utilizes continued fractions and tessellations
Reduces computational complexity
Abstract
Iku Nakamura [Hilbert schemes of Abelian group orbits, J. Alg. Geom. 10 (2001), 757--779] introduced the G-Hilbert scheme for a finite subgroup G in SL(3,C), and conjectured that it is a crepant resolution of the quotient C^3/G. He proved this for a diagonal Abelian group A by introducing an explicit algorithm that calculates A-Hilb C^3. This note calculates A-Hilb C^3 much more simply, in terms of fun with continued fractions plus regular tesselations by equilateral triangles.
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 Geometry and Number Theory · Advanced Algebra and Geometry · Finite Group Theory Research