Invariance property of orbifold elliptic genus for multi-fans

Details Invariance property of orbifold elliptic genus for multi-fans Invariance property of orbifold elliptic genus for multi-fans

2007-11-28

arxiv.org/abs/0711.4481v1

Mathematics

Algebraic Topology

38 pages. Expanded version of the talk at Toric Topology Conference

Scientific paper

Multi-fan is an analogous notion of fan. As a fan is associated to a toric variety a multi-fan is associated to a torus orbifold. Orbifold elliptic class and orbifold elliptic genus are defined for a triple of a multi-fan, a set of generating integral vectors of one dimensional cones and a $\mathbb{Q}$ divisor. They are shown to behave functorially with respect to birational morphisms between these triples. The result may be considered as a combinatorial or topological analogue of the main result of Borisov and Libgober, McKay correspondence for elliptic genera, Ann. of Math., 161 (2005).

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