Automorphism loci for the moduli space of rational maps
Nikita Miasnikov, Brian Stout, and Phillip Williams

TL;DR
This paper characterizes automorphism groups and singularities in the moduli space of degree d rational maps, determining possible automorphism groups, their loci, and implications for the space's geometric and algebraic structure.
Contribution
It provides a detailed description of automorphism loci, classifies possible automorphism groups, and analyzes singularities in the moduli space of rational maps.
Findings
Classified subgroups of automorphism groups for rational maps.
Determined dimensions of automorphism loci and singular loci.
Computed Picard and class groups of the moduli spaces.
Abstract
Let be an algebraically closed field of characteristic and the moduli space of rational maps on of degree over . This paper describes the automorphism loci and and the singular locus . In particular, we determine which groups occur as subgroups of the automorphism group of some for a given and calculate the dimension of the locus. Next, we prove an analogous theorem to the Rauch-Popp-Oort characterization of singular points on the moduli scheme for curves. The results concerning these distinguished loci are used to compute the Picard and class groups of and .
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.
