@article{6d05efdd8222428996dade6148ee04d7,
title = "D-critical locus structure on the Hilbert schemes of some local toric Calabi-Yau threefolds",
abstract = "The notion of a d-critical locus is an ingredient in the definition of motivic Donaldson-Thomas invariants by [6]. In this paper we show that there is a d-critical locus structure on the Hilbert scheme of dimension zero subschemes on some local toric Calabi-Yau 3-folds. We also show that using this d-critical locus structure and a choice of orientation data, the resulting motivic invariants agree with the definition given by the previous work of [2].",
author = "Sheldon Katz and Yun Shi",
note = "We thank Ben Davison for helpful discussions on this subject and motivic DT theory in general and Tony Pantev for helpful conversations about \u22121-shifted symplectic structures. We are also grateful for Bal\u00E1zs Szendro\u030Bi for helpful comments on a previous version of this paper. The research of the first author is supported in part by NSF grants DMS\u20131802242 and DMS\u20132201203, as well as by NSF grant DMS-1440140 while in residence at MSRI in Spring, 2018. Both authors would like to thank MSRI for the excellent working environment. The second author is grateful for the mini course given by Kai Behrend during the program Enumerative Geometry beyond Numbers at MSRI, where she first learned this problem. Part of 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 = "2024",
doi = "10.4310/MRL.241211045305",
language = "English (US)",
volume = "31",
pages = "1493--1522",
journal = "Mathematical Research Letters",
issn = "1073-2780",
publisher = "International Press, Inc.",
number = "5",
}