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arXiv · 2405.10092

A motivic integral identity for $(-1)$-shifted symplectic stacks

Chenjing Bu
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Abstract

We prove a motivic integral identity relating the motivic Behrend function of a $(-1)$-shifted symplectic stack to that of its stack of graded points. This generalizes analogous identities for moduli stacks of objects in $3$-Calabi$\unicode{x2013}$Yau abelian categories obtained by Kontsevich$\unicode{x2013}$Soibelman and Joyce$\unicode{x2013}$Song, which are crucial in proving wall-crossing formulae for Donaldson$\unicode{x2013}$Thomas invariants. We expect our identity to be useful in extending motivic Donaldson$\unicode{x2013}$Thomas theory to general $(-1)$-shifted symplectic stacks.

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Chenjing Bu. 2024-05-16. A motivic integral identity for $(-1)$-shifted symplectic stacks. https://doi.org/10.1112/mod.2025.10009

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