Stacky GKM Graphs and Orbifold Gromov-Witten Theory

Artan Sheshmani present new results on arXiv in collaboration with Chiu-Chu Melissa Liu

2018.07.24 | Christine Dilling

Following Zong (arXiv:1604.07270), we define an algebraic GKM orbifold X to be a smooth Deligne-Mumford stack equipped with an action of an algebraic torus T, with only finitely many zero-dimensional and one-dimensional orbits. The 1-skeleton of X is the union of its zero-dimensional and one-dimensional T-orbits; its formal neighborhood X^ in X determines a decorated graph, called the stacky GKM graph of X. The T-equivariant orbifold Gromov-Witten (GW) invariants of X can be computed by localization and depend only on the stacky GKM graph of X with the T-action. 

We also introduce abstract stacky GKM graphs and define their formal equivariant orbifold GW invariants. Formal equivariant orbifold GW invariants of the stacky GKM graph of an algebraic GKM orbifold X are refinements of T-equivariant orbifold GW invariants of X.  

Link to the paper on arXiv