Computing invariants via slicing groupoids: Gel'fand MacPherson, Gale and positive characteristic stable maps

TL;DR

This paper introduces a groupoid-based method for computing invariants, illustrating it through classical correspondences and describing moduli spaces, including explicit cases over integers and in positive characteristic.

Contribution

It develops a novel groupoid-theoretic framework for invariants, connecting classical geometric correspondences with explicit descriptions of moduli spaces in various characteristics.

Findings

Describes the Gel'fand-MacPherson correspondence using groupoids

Provides Zariski-local descriptions of moduli spaces of points in P^1

Identifies singularities in characteristic 2 related to the Veronese cone

Abstract

We offer a groupoid-theoretic approach to computing invariants. We illustrate this approach by describing the Gel'fand-MacPherson correspondence and the Gale transform as well as giving Zariski-local descriptions of the moduli space of ordered points in P^1. We give an explicit description of the moduli space M_0(P^1,2) over Spec Z. In characteristic 2, there is a singularity at the totally ramified cover which is isomorphic to the affine cone over the Veronese embedding P^1 --> P^4.