  We establish cosection localization and vanishing results for virtual
fundamental classes of derived manifolds, combining the theory of derived
differential geometry by Joyce with the theory of cosection localization by
Kiem-Li. As an application, we show that the stable pair invariants of
hyperk\"{a}hler fourfolds, defined by Cao-Maulik-Toda, are zero.

Algebraic Geometry;Differential Geometry