The notion of a d-critical locus is an ingredient in the definition of motivic Donaldson–Thomas invariants by Bussi-Joyce-Meinhardt. 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 (Formula presented.) -shifted symplectic structure on the derived moduli stack. 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. In particular, the canonical d-critical locus structure is isomorphic to the one constructed in a previous paper by the authors for local (Formula presented.) and local (Formula presented.).
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