@article{6ccbcbd92a1142a093eeb66c0bd98b73,
title = "Deformations of log canonical and f-pure singularities",
abstract = "We introduce a lifting property for local cohomology which leads to a unified treatment of the dualizing complex for at morphisms with semi-log-canonical, Du Bois or F-pure fibers. As a consequence, we obtain that in all three cases, the cohomology sheaves of the relative dualizing complex are at and commute with base change. We also derive several consequences for deformations of semi-log-canonical, Du Bois and F-pure singularities.",
keywords = "Du bois, F-pure, Log canonical",
author = "J{\`a}nos Koll{\`a}r and Kov{\`a}csc, {S{\`a}ndor J.}",
note = "Funding Information: J{\'a}nos Koll{\'a}r was supported in part by NSF Grants DMS-1362960 and DMS-1901855. S{\'a}ndor Kov{\'a}cs was supported in part by NSF Grant DMS-1565352 and the Craig McKibben and Sarah Merner Endowed Professorship in Mathematics. Funding Information: J{\`a}nos Koll{\`a}r was supported in part by NSF Grants DMS-1362960 and DMS-1901855. S{\`a}ndor Kov{\`a}cs was supported in part by NSF Grant DMS-1565352 and the Craig McKibben and Sarah Merner Endowed Professorship in Mathematics. We would like to thank Johan de Jong for comments and discussions from which we have greatly benefited and for supplying several results we needed in [Sta20]. We would also like to thank Linquan Ma and Karl Schwede for pointing us to [MSS17, Remark 3.4] and for numerous useful discussions about F-singularities, and the referee for suggesting several improvements to the exposition. Publisher Copyright: {\textcopyright} 2020 European Mathematical Society Publishing House.",
year = "2020",
doi = "10.14231/AG-2020-027",
language = "English (US)",
volume = "7",
pages = "758--780",
journal = "Algebraic Geometry",
issn = "2313-1691",
publisher = "European Mathematical Society Publishing House",
number = "6",
}