Topological invariants of orbifold toric varieties

Research Group Harada

May 8 - 29, 2011

Participants: David Anderson, Anthony Bahri, Matthias Franz, Megumi Harada, Tara Suzanne Holm, Sam Payne, Nigel Ray, Gareth Williams

The research group took an interdisciplinary approach to the study of weighted projective spaces and, more generally, to orbifold toric varieties and toric Deligne-Mumford stacks.

The computation of stringy / stacky / orbifold topological invariants of orbifolds is currently actively studied in many different fields, such as algebraic geometry, algebraic topology, and symplectic geometry.

The aim of the research group was

• to unify as much as possible the different viewpoints on these spaces, thus effectively building a common framework, language, and toolkit for their study, and
• to rectify the current shortage of explicit computations of such algebraic / topological invariants by providing concrete descriptions (for example via explicit generators and relations) for important families of examples.