@article{cb67b22766574f02a5b70ef516b52f9f,
title = "Blowups with log canonical singularities",
abstract = "We show that the minimum weight of a weighted blowup of Ad with ε–log canonical singularities is bounded by a constant depending only on ε and d . This was conjectured by Birkar. Using the recent classification of 4–dimensional empty simplices by Iglesias-Vali{\~n}o and Santos, we work out an explicit bound for blowups of A4 with terminal singular-ities: the smallest weight is always at most 32, and at most 6 in all but finitely many cases.",
author = "Gregory Sankaran and Francisco Santos",
note = "Funding Information: Some background on birational geometry was supplied to Sankaran by Anne-Sophie Kaloghiros. The explanations here relating these results to their wider context are largely hers, but errors and omissions in such explanations are definitely ours. Parts of this work were carried out while Sankaran was visiting Fukuoka University and KIAS, Seoul: he thanks both for hospitality and a helpful environment. Work of Santos was supported by grant MTM2017-83750-P of the Spanish Ministry of Economy and Competitiveness and by the Einstein Foundation Berlin under grant EVF-2015-230. We also thank the organisers of MEGA 2019 (Madrid), where the two authors first met and discussed these questions. ",
year = "2021",
month = jul,
day = "12",
doi = "10.2140/gt.2021.25.2145",
language = "English",
volume = "25",
pages = "2145--2166",
journal = "Geometry & Topology",
issn = "1465-3060",
publisher = "University of Warwick",
number = "4",
}
