Homology of moduli stacks of complexes

Date
2019/08/06 Tue 15:00 - 16:30
Room
6号館609号室
Speaker
Jacob Gross
Affiliation
University of Oxford
Abstract

Dominic Joyce recently proved that the homology of moduli stacks of objects in certain dg-categories carries the structure of a graded vertex algebra. We analyse the example of the derived category of a smooth complex projective variety X, obtaining that for curves, surfaces, and certain 3- and 4-folds Joyce's construction gives a generalised super-lattice vertex algebra associated to the topological K-theory of X. These calculations are made possible by demonstrating that the Betti realization of the moduli stack of objects in the derived category of X is a homotopy-theoretic group completion of the moduli space of globally generated algebraic vector bundles on X.