TY - JOUR
T1 - Collapsing of negative Kähler-Einstein metrics
AU - Zhang, Yuguang
N1 - Publisher Copyright:
© 2015, International Press of Boston, Inc. All rights reserved.
PY - 2015
Y1 - 2015
N2 - In this paper, we study the collapsing behaviour of negative Kähler-Einstein metrics along degenerations of canonical polarized manifolds. We prove that for a toroidal degeneration of canonical polarized manifolds with the total space Q-factorial, the Kähler-Einstein metrics on fibers collapse to a lower dimensional complete Riemannian manifold in the pointed Gromov-Hausdorff sense by suitably choosing the base points. Furthermore, the most collapsed limit is a real affine Kähler manifold.
AB - In this paper, we study the collapsing behaviour of negative Kähler-Einstein metrics along degenerations of canonical polarized manifolds. We prove that for a toroidal degeneration of canonical polarized manifolds with the total space Q-factorial, the Kähler-Einstein metrics on fibers collapse to a lower dimensional complete Riemannian manifold in the pointed Gromov-Hausdorff sense by suitably choosing the base points. Furthermore, the most collapsed limit is a real affine Kähler manifold.
UR - http://www.scopus.com/inward/record.url?scp=84973369653&partnerID=8YFLogxK
U2 - 10.4310/MRL.2015.v22.n6.a16
DO - 10.4310/MRL.2015.v22.n6.a16
M3 - Article
AN - SCOPUS:84973369653
SN - 1073-2780
VL - 22
SP - 1843
EP - 1869
JO - Mathematical Research Letters
JF - Mathematical Research Letters
IS - 6
ER -