Artin group actions on derived categories of threefolds

Abstract

Motivated by the enhanced gauge symmetry phenomenon of the physics literature and mirror symmetry, this paper constructs an action of an Artin group on the derived category of coherent sheaves of a smooth quasiprojective threefold containing a configuration of ruled surfaces described by a finite type Dynkin diagram. The action extends over deformations of the threefold via a compatible action of the corresponding reflection group on the base of its deformation space. All finite type Dynkin diagrams are realized.

Derived category automorphisms from mirror symmetry

“…We make no attempt to relate this work to these developments, although there seem to be many interesting connections. We only mention the papers [42], [43], [17], [5], which are intimately related to the results of the present work and provide more applications than those presented in the last section of this paper.…”

Enhanced Gauge Symmetry and Braid Group Actions

“…It is possible to show (see [22,Theorem 4.1] for the case of threefolds) that the kernels U i,s are restrictions to the fibres of a relative kernel…”

“…Proof The proof, given in detail in [22,Section 4], is similar to that of Theorem 3.2. The individual functors U j,s are defined using a diagram…”

Aspects of Calabi-Yau Integrable and Hitchin Systems

“…A closely related construction, without the C-action, appeared in [17] inspired by [40]. Instead of commenting on the proof of this proposition, we give an example.…”