Extremal Kähler metrics on blow-ups of parabolic ruled surfaces
Bulletin de la Société Mathématique de France, Volume 141 (2013) no. 3, p. 481-516

New examples of extremal Kähler metrics are given on blow-ups of parabolic ruled surfaces. The method used is based on the gluing construction of Arezzo, Pacard and Singer [5]. This enables to endow ruled surfaces of the form (𝒪L) with special parabolic structures such that the associated iterated blow-up admits an extremal metric of non-constant scalar curvature.

De nouveaux exemples de métriques de Kähler extrémales sont donnés sur des éclatements de surfaces réglées paraboliques. La technique utilisée est basée sur la méthode de recollement de Arezzo, Pacard et Singer [5]. Ceci permet de munir les surfaces réglées de la forme (𝒪L) de structures paraboliques particulières telles que les éclatements itérés associés supportent des métriques extrémales à courbure scalaire non constante.

DOI : https://doi.org/10.24033/bsmf.2654
Classification:  53C55,  32Q26
Keywords: extremal kähler metrics, Hirzebruch-Jung singularities, resolution, iterated blow-ups, parabolic structures
@article{BSMF_2013__141_3_481_0,
     author = {Tipler, Carl},
     title = {Extremal K\"ahler metrics on blow-ups of parabolic ruled surfaces},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {141},
     number = {3},
     year = {2013},
     pages = {481-516},
     doi = {10.24033/bsmf.2654},
     language = {en},
     url = {http://www.numdam.org/item/BSMF_2013__141_3_481_0}
}
Tipler, Carl. Extremal Kähler metrics on blow-ups of parabolic ruled surfaces. Bulletin de la Société Mathématique de France, Volume 141 (2013) no. 3, pp. 481-516. doi : 10.24033/bsmf.2654. http://www.numdam.org/item/BSMF_2013__141_3_481_0/

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