@article{c0074eca870143378efef15c8cc8dd24,
title = "Geometry of Twisted K{\"a}hler–Einstein Metrics and Collapsing",
abstract = "We prove that the twisted K{\"a}hler–Einstein metrics that arise on the base of certain holomorphic fiber space with Calabi–Yau fibers have conical-type singularities along the discriminant locus. These fiber spaces arise naturally when studying the collapsing of Ricci-flat K{\"a}hler metrics on Calabi–Yau manifolds, and of the K{\"a}hler–Ricci flow on compact K{\"a}hler manifolds with semiample canonical bundle and intermediate Kodaira dimension. Our results allow us to understand their collapsed Gromov–Hausdorff limits when the base is smooth and the discriminant has simple normal crossings.",
author = "Mark Gross and Valentino Tosatti and Yuguang Zhang",
note = "Funding Information: We are grateful to H. Guenancia, H.-J. Hein, D. Kim, M. Popa and P.M.H. Wilson for discussions. This work was done during the second-named author{\textquoteright}s visits to the Institut Henri Poincar{\'e} in Paris in 2018 (supported by a Chaire Poincar{\'e} at IHP funded by the Clay Mathematics Institute) and to the Center for Mathematical Sciences and Applications at Harvard University in 2018, and during the third-named author{\textquoteright}s visit to Northwestern University in 2016, which we would like to thank for the hospitality and support. Mark Gross was supported by EPSRC Grant EP/N03189X/1 and a Royal Society Wolfson Research Merit Award. Valentino Tosatti was also partially supported by NSF Grants DMS-1610278 and DMS-1903147. Yuguang Zhang was supported by the Simons Foundation{\textquoteright}s program Simons Collaboration on Special Holonomy in Geometry, Analysis and Physics (Grant #488620). Publisher Copyright: {\textcopyright} 2020, Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2020",
month = dec,
doi = "10.1007/s00220-020-03911-0",
language = "English (US)",
volume = "380",
pages = "1401--1438",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer New York",
number = "3",
}