The Kahler-Ricci flow on Fano bundles

被引：5
|
作者：
Fu, Xin [1 ]
Zhang, Shijin [2 ]
机构：
[1] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA
[2] Beihang Univ, Sch Math & Syst Sci, Beijing 100191, Peoples R China
来源：
MATHEMATISCHE ZEITSCHRIFT | 2017年 / 286卷 / 3-4期
基金：
高等学校博士学科点专项科研基金;
关键词：
CONTRACTING EXCEPTIONAL DIVISORS; FINITE-TIME SINGULARITY; LOG GENERAL TYPE; EINSTEIN MANIFOLDS; SCALAR CURVATURE; MINIMAL MODELS; VARIETIES; EXISTENCE; SURFACES; CONVERGENCE;
D O I：
10.1007/s00209-017-1881-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the behavior of the kahler-Ricci flow on some Fano bundles which is a trivial bundle on one Zariski open set. We show that if the fiber is P-m blown up at one point or some weighted projective space blown up at the orbifold point and the initial metric is in a suitable Kahler class, then the fibers collapse in finite time and the metrics converge sub-sequentially in Gromov-Hausdorff sense to a metric on the base.
引用
收藏
页码：1605 / 1626
页数：22
相关论文
共 50 条
  • [21] Stability of Kahler-Ricci Flow
    Chen, Xiuxiong
    Li, Haozhao
    JOURNAL OF GEOMETRIC ANALYSIS, 2010, 20 (02) : 306 - 334
  • [22] Characterization of Einstein-Fano Manifolds via the Kahler-Ricci Flow
    Pali, Nefton
    INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2008, 57 (07) : 3241 - 3274
  • [23] Notes on Kahler-Ricci Flow
    Tian, Gang
    RICCI FLOW AND GEOMETRIC APPLICATIONS, 2016, 2166 : 105 - 136
  • [24] KAHLER-RICCI SOLITONS ON CERTAIN TORIC BUNDLES
    Nakagawa, Yasuhiro
    KYUSHU JOURNAL OF MATHEMATICS, 2019, 73 (02) : 379 - 390
  • [25] Regularity of the Kahler-Ricci flow
    Tian, Gang
    Zhang, Zhenlei
    COMPTES RENDUS MATHEMATIQUE, 2013, 351 (15-16) : 635 - 638
  • [26] Convergence of a Kahler-Ricci flow
    Sesum, N
    MATHEMATICAL RESEARCH LETTERS, 2005, 12 (5-6) : 623 - 632
  • [27] The twisted Kahler-Ricci flow
    Collins, Tristan C.
    Szekelyhidi, Gabor
    JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2016, 716 : 179 - 205
  • [28] A modified Kahler-Ricci flow
    Zhang, Zhou
    MATHEMATISCHE ANNALEN, 2009, 345 (03) : 559 - 579
  • [29] An Introduction to the Kahler-Ricci Flow
    Song, Jian
    Weinkove, Ben
    INTRODUCTION TO THE KAHLER-RICCI FLOW, 2013, 2086 : 89 - 188
  • [30] Monotonicity and Kahler-Ricci flow
    Ni, L
    GEOMETRIC EVOLUTION EQUATIONS, 2005, 367 : 149 - 165
12345