TY - JOUR
T1 - Geometry of Twisted Kähler–Einstein Metrics and Collapsing
AU - Gross, Mark
AU - Tosatti, Valentino
AU - Zhang, Yuguang
N1 - Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/12
Y1 - 2020/12
N2 - We prove that the twisted Kähler–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 Kähler metrics on Calabi–Yau manifolds, and of the Kähler–Ricci flow on compact Kähler 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.
AB - We prove that the twisted Kähler–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 Kähler metrics on Calabi–Yau manifolds, and of the Kähler–Ricci flow on compact Kähler 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.
UR - http://www.scopus.com/inward/record.url?scp=85095678349&partnerID=8YFLogxK
U2 - 10.1007/s00220-020-03911-0
DO - 10.1007/s00220-020-03911-0
M3 - Article
AN - SCOPUS:85095678349
SN - 0010-3616
VL - 380
SP - 1401
EP - 1438
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 3
ER -