Scalar Flat Kähler Metrics on Affine Bundles over CP¹
We show that the total space of any affine C-bundle over CP¹ with negative degree admits an ALE scalar-flat Kähler metric. Here the degree of an affine bundle means the negative of the self-intersection number of the section at infinity in a natural compactification of the bundle, and so for line bu...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2014 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2014
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146689 |
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| Zitieren: | Scalar Flat Kähler Metrics on Affine Bundles over CP¹ / N. Honda // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 14 назв. — англ. |
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Honda, N. 2019-02-10T18:55:07Z 2019-02-10T18:55:07Z 2014 Scalar Flat Kähler Metrics on Affine Bundles over CP¹ / N. Honda // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 14 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53A30 DOI:10.3842/SIGMA.2014.046 https://nasplib.isofts.kiev.ua/handle/123456789/146689 We show that the total space of any affine C-bundle over CP¹ with negative degree admits an ALE scalar-flat Kähler metric. Here the degree of an affine bundle means the negative of the self-intersection number of the section at infinity in a natural compactification of the bundle, and so for line bundles it agrees with the usual notion of the degree. This paper is a contribution to the Special Issue on Progress in Twistor Theory. The full collection is available at http://www.emis.de/journals/SIGMA/twistors.html. I would like to thank Jef f Viaclovsky for numerous useful discussion from which this work has originated. Also I would like to thank Akira Fujiki for invaluable comments on deformations of line bundles. This work was supported by JSPS KAKENHI Grant Number 24540061. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Scalar Flat Kähler Metrics on Affine Bundles over CP¹ Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Scalar Flat Kähler Metrics on Affine Bundles over CP¹ |
| spellingShingle |
Scalar Flat Kähler Metrics on Affine Bundles over CP¹ Honda, N. |
| title_short |
Scalar Flat Kähler Metrics on Affine Bundles over CP¹ |
| title_full |
Scalar Flat Kähler Metrics on Affine Bundles over CP¹ |
| title_fullStr |
Scalar Flat Kähler Metrics on Affine Bundles over CP¹ |
| title_full_unstemmed |
Scalar Flat Kähler Metrics on Affine Bundles over CP¹ |
| title_sort |
scalar flat kähler metrics on affine bundles over cp¹ |
| author |
Honda, N. |
| author_facet |
Honda, N. |
| publishDate |
2014 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We show that the total space of any affine C-bundle over CP¹ with negative degree admits an ALE scalar-flat Kähler metric. Here the degree of an affine bundle means the negative of the self-intersection number of the section at infinity in a natural compactification of the bundle, and so for line bundles it agrees with the usual notion of the degree.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146689 |
| citation_txt |
Scalar Flat Kähler Metrics on Affine Bundles over CP¹ / N. Honda // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 14 назв. — англ. |
| work_keys_str_mv |
AT hondan scalarflatkahlermetricsonaffinebundlesovercp1 |
| first_indexed |
2025-11-30T15:31:13Z |
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2025-11-30T15:31:13Z |
| _version_ |
1850857973258125312 |