@article{2c8b024f2bed42cfb46588d14bd8e937,
title = "Divisors computing minimal log discrepancies on lc surfaces",
abstract = "Let be an lc surface germ. If is klt, we show that there exists a divisor computing the minimal log discrepancy of that is a Koll{\'a}r component of. If or is not Du Val, we show that any divisor computing the minimal log discrepancy of is a potential lc place of. This extends a result of Blum and Kawakita who independently showed that any divisor computing the minimal log discrepancy on a smooth surface is a potential lc place.",
keywords = "14E30 14B05",
author = "Jihao Liu and Lingyao Xie",
note = "Funding Information: The authors would like to thank Christopher D. Hacon for useful discussions and encouragements. The first author would like to thank Harold Blum, Jingjun Han, Yuchen Liu, Chenyang Xu, and Ziquan Zhuang for inspiration on Questions 1·1 and 1·3 and useful discussions. The authors would like to thank Jingjun Han for useful comments. Special thank to Ziquan Zhuang who kindly shares Example 6·1 after the first version of the paper was posted on arXiv. The authors were partially supported by NSF research grants no: DMS-1801851, DMS-1952522 and by a grant from the Simons Foundation; award Number: 256202. Publisher Copyright: {\textcopyright} The Author(s), 2023. Published by Cambridge University Press on behalf of Cambridge Philosophical Society.",
year = "2023",
month = jul,
day = "14",
doi = "10.1017/S0305004123000051",
language = "English (US)",
volume = "175",
pages = "107--128",
journal = "Mathematical Proceedings of the Cambridge Philosophical Society",
issn = "0305-0041",
publisher = "Cambridge University Press",
number = "1",
}