A motivic integral identity for -shifted symplectic stacks

Journal article

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

Authors: Bu, C

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Cambridge University Press
• Journal: Moduli
• Volume: 2
• Article number: e16
• Publication date: 2025-11-04
• Acceptance date: 2025-02-04
• DOI: 10.1112/mod.2025.10009
• EISSN: 2977-1382
• ISSN: 2949-7647
• Language: English
• Keywords: motivic vanishing cycle; shifted symplectic stack; Behrend function; motivic integration; Donaldson–Thomas invariant; 14N35