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.

25 pages, 2 figures, one inaccuracy corrected

References in corpus (5)

• Semiorthogonal decomposition for algebraic varieties
• Hypergeometric functions and mirror symmetry in toric varieties
• Derived Category Automorphisms from Mirror Symmetry
• Enhanced gauge symmetry and braid group actions
• Calabi-Yau threefolds with a curve of singularities and counterexamples to the Torelli problem