D-critical loci for local toric Calabi-Yau 3-folds

Abstract

The notion of a d-critical locus is an ingredient in the definition of motivic Donaldson-Thomas invariants by [BJM19]. There is a canonical d-critical locus structure on the Hilbert scheme of dimension zero subschemes on local toric Calabi-Yau 3-folds. This is obtained by truncating the $-1$-shifted symplectic structure on the derived moduli stack [BBBBJ15]. In this paper we show the canonical d-critical locus structure has critical charts consistent with the description of Hilbert scheme as a degeneracy locus [BBS13]. In particular, the canonical d-critical locus structure is isomorphic to the one constructed in [KS12] for local ${\mathbb{P}}^2$ and local ${\mathbb{F}}_n$.

References in corpus (6)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Calabi-Yau algebras
• A 'Darboux Theorem' for shifted symplectic structures on derived Artin stacks, with applications
• Invariance of orientation data for ind-constructible Calabi-Yau $A_{\infty }$ categories under derived equivalence
• Orientation data for coherent sheaves on the local projective plane
• D-critical locus structure on the Hilbert schemes of some local toric Calabi-Yau threefolds