Derived category of moduli of pointed curves -- II

TL;DR

This paper proves that the moduli space of stable rational curves with n marked points admits a full exceptional collection that is symmetric under permutations, revealing its K-group structure as a permutation lattice.

Contribution

It establishes the existence of a symmetric full exceptional collection in the derived category of the moduli space, advancing understanding of its algebraic and geometric structure.

Findings

Full exceptional collection exists and is symmetric under S_n

K-group is a permutation S_n-lattice

Enhances understanding of moduli space's derived category

Abstract

We show that the moduli space of stable rational curves with $n$ marked points has a full exceptional collection equivariant under the action of the symmetric group $S_n$ permuting the marked points. In particular, its K-group with integer coefficients is a permutation $S_n$-lattice.