Derived category of moduli of pointed curves: II

Abstract

Abstract We prove a conjecture of Manin and Orlov: the moduli space script upper M overbar Subscript 0 comma n M¯0,n $\overline{\mathcal{M}}_{0,n}$ of stable rational curves with n marked points admits a full exceptional collection that is equivariant under the action of the symmetric group upper S Subscript n Sn $S_n$ permuting the marked points. In particular, its upper K 0 K0 $K_0$ -group with integral coefficients is a permutation upper S Subscript n Sn $S_n$ -lattice.