数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (1): 169-176.doi: 10.1016/S0252-9602(17)30124-8

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A NOTE ON CONICAL KÄHLER-RICCI FLOW ON MINIMAL ELLIPTIC KÄHLER SURFACES

张雅山   

  1. Department of Mathematics, University of Macau, Macau, China
  • 收稿日期:2016-11-01 修回日期:2017-03-28 出版日期:2018-02-25 发布日期:2018-02-25
  • 作者简介:Yashan ZHANG,E-mail:yashanzh@163.com
  • 基金资助:

    The research is partially supported by the Science and Technology Development Fund (Macao S.A.R.), Grant FDCT/016/2013/A1 and the Project MYRG2015-00235-FST of the University of Macau.

A NOTE ON CONICAL KÄHLER-RICCI FLOW ON MINIMAL ELLIPTIC KÄHLER SURFACES

Yashan ZHANG   

  1. Department of Mathematics, University of Macau, Macau, China
  • Received:2016-11-01 Revised:2017-03-28 Online:2018-02-25 Published:2018-02-25
  • Supported by:

    The research is partially supported by the Science and Technology Development Fund (Macao S.A.R.), Grant FDCT/016/2013/A1 and the Project MYRG2015-00235-FST of the University of Macau.

摘要:

We prove that, under a semi-ampleness type assumption on the twisted canonical line bundle, the conical Kähler-Ricci flow on a minimal elliptic Kähler surface converges in the sense of currents to a generalized conical Kähler-Einstein on its canonical model. Moreover, the convergence takes place smoothly outside the singular fibers and the chosen divisor.

关键词: conical Kähler-Ricci flow, Kähler-Einstein metric, minimal elliptic surface

Abstract:

We prove that, under a semi-ampleness type assumption on the twisted canonical line bundle, the conical Kähler-Ricci flow on a minimal elliptic Kähler surface converges in the sense of currents to a generalized conical Kähler-Einstein on its canonical model. Moreover, the convergence takes place smoothly outside the singular fibers and the chosen divisor.

Key words: conical Kähler-Ricci flow, Kähler-Einstein metric, minimal elliptic surface