Derived category of moduli of pointed curves -- I

TL;DR

This paper explores the derived category of moduli spaces of genus 0 curves with marked points, developing equivariant descriptions and constructing an exceptional collection on the Losev-Manin space.

Contribution

It introduces an equivariant framework for the derived category of these moduli spaces and constructs a full exceptional collection categorifying derangements.

Findings

Constructed an equivariant full exceptional collection on the Losev-Manin space.

Developed multiple approaches to describe the derived category equivariantly.

Categorified derangements through the exceptional collection.

Abstract

This is the first paper in the sequence devoted to derived category of moduli spaces of curves of genus $0$ with marked points. We develop several approaches to describe it equivariantly with respect to the action of the symmetric group permuting marked points. We construct an equivariant full exceptional collection on the Losev-Manin space which categorifies derangements.