BPS state counting on singular varieties
Elizabeth Gasparim, Thomas K\"oppe, Pushan Majumdar, Koushik Ray
TL;DR
This paper introduces new partition functions for theories on toric singularities, constructed from crepant resolutions, and demonstrates their homogeneity properties through explicit examples.
Contribution
It presents a novel method to define partition functions on singular varieties using crepant resolutions, revealing their homogeneous structure.
Findings
Partition functions are homogeneous on MacMahon factors.
Explicit computations confirm the new partition functions' properties.
Abstract
We define new partition functions for theories with targets on toric singularities via products of old partition functions on crepant resolutions. We compute explicit examples and show that the new partition functions turn out to be homogeneous on MacMahon factors.
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