@article{79da24eec7684888acc5eb297c2394cb,
title = "D-critical loci for length n sheaves on 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 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.).",
author = "Sheldon Katz and Yun Shi",
note = "We would like to thank Nachiketa Adhikari and Aron Heleodoro for helpful conversations, and especially Tony Pantev for helpful conversations about derived algebraic geometry and for suggesting improvements to the paper. We would also like to thank the referee for their suggestions which improved the exposition. The research of the first author is supported by NSF grant DMS‐1802242. The second author would like to thank Dhyan Aranha and Ningchuan Zhang for helpful conversations on derived geometry, and Ben Davison for teaching her the bimodule resolution at MSRI. The work was done while the second author was a postdoc at CMSA, Harvard. She would like to thank CMSA for the excellent working environment. We would like to thank Nachiketa Adhikari and Aron Heleodoro for helpful conversations, and especially Tony Pantev for helpful conversations about derived algebraic geometry and for suggesting improvements to the paper. We would also like to thank the referee for their suggestions which improved the exposition. The research of the first author is supported by NSF grant DMS-1802242. The second author would like to thank Dhyan Aranha and Ningchuan Zhang for helpful conversations on derived geometry, and Ben Davison for teaching her the bimodule resolution at MSRI. The work was done while the second author was a postdoc at CMSA, Harvard. She would like to thank CMSA for the excellent working environment.",
year = "2022",
month = dec,
doi = "10.1112/blms.12680",
language = "English (US)",
volume = "54",
pages = "2101--2116",
journal = "Bulletin of the London Mathematical Society",
issn = "0024-6093",
publisher = "John Wiley & Sons, Ltd.",
number = "6",
}