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 $\mathbb{F}_n$.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2021
- DOI:
- 10.48550/arXiv.2108.13510
- arXiv:
- arXiv:2108.13510
- Bibcode:
- 2021arXiv210813510K
- Keywords:
-
- Mathematics - Algebraic Geometry