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arXiv · 2508.12128

The 4-fold Pandharipande--Thomas vertex and Jeffrey--Kirwan residue

Taro Kimura·Go Noshita
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Abstract

We present a contour integral formalism for computing the K-theoretic equivariant Pandharipande--Thomas (PT) 4-vertex. Within the Jeffrey--Kirwan (JK) residue framework, we show that the PT 4-vertex can be obtained from the same integrand as the Donaldson--Thomas (DT) 4-vertex by choosing a different reference vector. We illustrate the formalism through examples involving curves and surfaces on the 4-fold. Furthermore, we investigate the DT/PT correspondence for the 4-fold setting together with its higher rank and supergroup-like generalizations.

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Taro Kimura, Go Noshita. 2025-08-16. The 4-fold Pandharipande--Thomas vertex and Jeffrey--Kirwan residue. https://doi.org/10.1007/s11005-026-02071-x

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