Scalar-flat Kähler surfaces of all genera

Jongsu Kim; Claude LeBrun; Massimiliano Pontecorvo

Scalar-flat Kähler surfaces of all genera

Jongsu Kim
, Claude LeBrun
, Massimiliano Pontecorvo

Mathematics

Stony Brook University

Sogang University
Roma Tre University

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

Abstract

Let (M, J) be a compact complex 2-manifold which admits a Kähler metric for which the integral of the scalar curvature is non-negative. Also suppose that M does not admit a Ricci-flat Kähler metric. Then if M is blown up at sufficiently many points, the resulting complex surface (M̃, J̃) admits Kähler metrics with scalar curvature identically equal to zero. This proves Conjecture 1 of [16].

Original language	English
Pages (from-to)	69-95
Number of pages	27
Journal	Journal fur die Reine und Angewandte Mathematik
Volume	486
State	Published - 1997

Cite this

@article{af8dba1a56f14e8f9bc912f98f7d8c8a,

title = "Scalar-flat K{\"a}hler surfaces of all genera",

abstract = "Let (M, J) be a compact complex 2-manifold which admits a K{\"a}hler metric for which the integral of the scalar curvature is non-negative. Also suppose that M does not admit a Ricci-flat K{\"a}hler metric. Then if M is blown up at sufficiently many points, the resulting complex surface ({\~M}, {\~J}) admits K{\"a}hler metrics with scalar curvature identically equal to zero. This proves Conjecture 1 of [16].",

author = "Jongsu Kim and Claude LeBrun and Massimiliano Pontecorvo",

year = "1997",

language = "English",

volume = "486",

pages = "69--95",

journal = "Journal fur die Reine und Angewandte Mathematik",

issn = "0075-4102",

publisher = "Walter de Gruyter GmbH",

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TY - JOUR

T1 - Scalar-flat Kähler surfaces of all genera

AU - Kim, Jongsu

AU - LeBrun, Claude

AU - Pontecorvo, Massimiliano

PY - 1997

Y1 - 1997

N2 - Let (M, J) be a compact complex 2-manifold which admits a Kähler metric for which the integral of the scalar curvature is non-negative. Also suppose that M does not admit a Ricci-flat Kähler metric. Then if M is blown up at sufficiently many points, the resulting complex surface (M̃, J̃) admits Kähler metrics with scalar curvature identically equal to zero. This proves Conjecture 1 of [16].

AB - Let (M, J) be a compact complex 2-manifold which admits a Kähler metric for which the integral of the scalar curvature is non-negative. Also suppose that M does not admit a Ricci-flat Kähler metric. Then if M is blown up at sufficiently many points, the resulting complex surface (M̃, J̃) admits Kähler metrics with scalar curvature identically equal to zero. This proves Conjecture 1 of [16].

UR - https://www.scopus.com/pages/publications/0031521589

M3 - Article

SN - 0075-4102

VL - 486

SP - 69

EP - 95

JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

ER -

Scalar-flat Kähler surfaces of all genera

Abstract

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