@article{0d9596a826d0461b84f4b6f419c2ea55,
title = "An optimal gap of minimal log discrepancies of threefold non-canonical singularities",
abstract = "We show that the minimal log discrepancy of any Q-Gorenstein non-canonical threefold is [Formula presented], which is an optimal bound.",
keywords = "Minimal log discrepancy, Singularity",
author = "Jihao Liu and Liudan Xiao",
note = "Funding Information: The first author would like to have a very special thank to Chen Jiang, who not only kindly shared the draft of his preprint [8] which is crucial to this paper, but also gave the author some essential ideas of Lemma 2.10 and Lemma 6.3. He would like to thank Jiaming Li for her important help in the proof of Theorem 3.1. Some intuitions of this work were provided by James McKernan when the first author attended the 2018 Fall Program of Moduli Spaces and Varieties in SCMS. He would like to thank James McKernan for the useful discussion and SCMS for their hospitality. Part of the work was done when the first author made an unofficial visit to the Mathematical Sciences Research Institute in Berkeley, California during the Spring 2019 semester, and he would like to thank his advisor Christopher D. Hacon for his significant support and warm encouragement. He would also like to thank Jingjun Han, Yuchen Liu, Vyacheslav V. Shokurov, Chenyang Xu, Chuyu Zhou and Ziquan Zhuang for discussions and comments during the preparation of this paper. The first author was partially supported by NSF research grants no: DMS-1801851, DMS-1265285 and by a grant from the Simons Foundation; Award Number: 256202. The second author would like to thank her manager Aleksey Sanin and VP Peeyush Ranjan in Google for their effort to read through this article, make sure this work does not have interest conflicts with Google, and allow her to finish this work in her spare time. The authors would like to thank the referees for carefully checking the details and many useful suggestions. Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",
year = "2021",
month = sep,
doi = "10.1016/j.jpaa.2021.106674",
language = "English (US)",
volume = "225",
journal = "Journal of Pure and Applied Algebra",
issn = "0022-4049",
publisher = "Elsevier",
number = "9",
}