Configuration spaces of complex and real spheres
Igor Dolgachev, Benjamin Howard

TL;DR
This paper investigates the geometric invariant theory quotient of multiple projective spaces under orthogonal group actions, linking it to configuration spaces of spheres through classical isomorphisms.
Contribution
It provides a new interpretation of these quotients as configuration spaces of spheres, connecting algebraic geometry with classical geometry.
Findings
Identifies the GIT-quotient with configuration spaces of spheres.
Establishes a classical isomorphism with the Inversive group.
Provides geometric insights into the structure of these quotient spaces.
Abstract
We study the GIT-quotient of the Cartesian power of projective space modulo the projective orthogonal group. A classical isomorphism of this group with the Inversive group of birational transformations of the projective space of one dimension less allows one to interpret these spaces as configuration spaces of complex or real spheres.
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
TopicsMathematics and Applications · Digital Image Processing Techniques · Advanced Theoretical and Applied Studies in Material Sciences and Geometry
