Quotient Stacks and String Orbifolds

String Orbifolds and Quotient Stacks

In this note we observe that, contrary to the usual lore, string orbifolds do not describe strings on quotient spaces, but rather seem to describe strings on objects called quotient stacks, a result that follows from simply unraveling definitions, and is further justified by a number of results. Quotient stacks are very closely related to quotient spaces; for example, when the orbifold group ac...

Discrete Torsion, Quotient Stacks, and String Orbifolds Lecture at Wisconsin-madison Workshop on Mathematical Aspects of Orbifold String Theory

The resolution property for schemes and stacks

We prove the equivalence of two fundamental properties of algebraic stacks: being a quotient stack in a strong sense, and the resolution property, which says that every coherent sheaf is a quotient of some vector bundle. Moreover, we prove these properties in the important special case of orbifolds whose associated algebraic space is a scheme. (Mathematics Subject Classification: Primary 14A20,...

Introduction to Orbifolds

Orbifolds lie at the intersection of many different areas of mathematics, including algebraic and differential geometry, topology, algebra and string theory. Orbifolds were first introduced into topology and differential geometry by Satake [6], who called them V-manifolds. Satake described them as topological spaces generalizing smooth manifolds and generalized concepts such as de Rham cohomolo...

String compactifications on Calabi-Yau stacks

In this paper we study string compactifications on Deligne-Mumford stacks. The basic idea is that all such stacks have presentations to which one can associate gauged sigma models, where the group gauged need be neither finite nor effectively-acting. Such presentations are not unique, and lead to physically distinct gauged sigma models; stacks classify universality classes of gauged sigma model...