Sheaves on P^1 x P^1, bigraded resolutions, and coadjoint orbits of loop groups
Roger Bielawski, Lorenz Schwachh\"ofer
TL;DR
This paper constructs a canonical resolution for certain sheaves on P^1 x P^1 and explores the associated Poisson structure, linking algebraic geometry with symplectic geometry.
Contribution
It introduces a canonical linear resolution for acyclic 1-dimensional sheaves on P^1 x P^1 and analyzes the natural Poisson structure that arises.
Findings
Established a canonical resolution for sheaves on P^1 x P^1
Identified a natural Poisson structure related to the sheaves
Connected sheaf theory with geometric structures like coadjoint orbits
Abstract
We construct a canonical linear resolution of acyclic 1-dimensional sheaves on P^1 x P^1 and discuss the resulting natural Poisson structure.
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
TopicsGeometric and Algebraic Topology · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry