On the geometry of orbifold Gromov-Witten invariants
Hsian-Hua Tseng
TL;DR
This paper explores how specific geometric structures like gerbes and root constructions influence the Gromov-Witten invariants of Deligne-Mumford stacks, discussing conjectures and recent progress in this area.
Contribution
It provides a survey of conjectures and recent developments on the impact of gerbes and root constructions on Gromov-Witten invariants.
Findings
Formulated conjectures relating geometric structures to Gromov-Witten invariants
Surveyed recent progress on these conjectures
Highlighted the influence of gerbes and root constructions
Abstract
We consider the question of how geometric structures of a Deligne-Mumford stack affect its Gromov-Witten invariants. The two geometric structures studied here are {\em gerbes} and {\em root constructions}. In both cases, we explain conjectures on Gromov-Witten theory for these stacks and survey some recent progress on these conjectures.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology