A Poincaré type Kähler metric on the complement of a simple normal crossing divisor , in a compact Kähler manifold , is a Kähler metric on with cusp singularity along . We relate the Futaki character for holomorphic vector fields parallel to the divisor, defined for any fixed Poincaré type Kähler class, to the classical Futaki character for the relative smooth class. As an application we express a numerical obstruction to the existence of extremal Poincaré type Kähler metrics, in terms of mean scalar curvatures and Futaki characters.
On appelle métrique kählérienne de type Poincaré, sur le complémentaire d’un diviseur à croisements normaux simples dans une variété kählérienne compacte , une métrique kählérienne sur à singularités cusp le long de . On relie le caractère de Futaki des champs de vecteurs holomorphes parallèles au diviseur, défini pour toute classe de Kähler de métriques de type Poincaré fixée, au caractère de Futaki classique de la classe lisse sous-jacente. On donne en application une obstruction numérique à l’existence de métriques extrémales de type Poincaré, exprimée en termes de courbures scalaires moyennes et de caractères de Futaki.
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Keywords: Extremal Kähler metrics, Poincaré type Kähler metrics, Futaki character/invariant, Yau–Tian–Donaldson conjecture.
Mot clés : Métriques kählériennes extrémales, métriques kählériennes de type Poincaré, caractère/invariant de Futaki, conjecture de Yau–Tian–Donaldson.
Auvray, Hugues 1
@article{AIF_2018__68_1_319_0, author = {Auvray, Hugues}, title = {Note on {Poincar\'e} type {Futaki} characters}, journal = {Annales de l'Institut Fourier}, pages = {319--344}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {68}, number = {1}, year = {2018}, doi = {10.5802/aif.3162}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3162/} }
TY - JOUR AU - Auvray, Hugues TI - Note on Poincaré type Futaki characters JO - Annales de l'Institut Fourier PY - 2018 SP - 319 EP - 344 VL - 68 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3162/ DO - 10.5802/aif.3162 LA - en ID - AIF_2018__68_1_319_0 ER -
%0 Journal Article %A Auvray, Hugues %T Note on Poincaré type Futaki characters %J Annales de l'Institut Fourier %D 2018 %P 319-344 %V 68 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3162/ %R 10.5802/aif.3162 %G en %F AIF_2018__68_1_319_0
Auvray, Hugues. Note on Poincaré type Futaki characters. Annales de l'Institut Fourier, Volume 68 (2018) no. 1, pp. 319-344. doi : 10.5802/aif.3162. https://aif.centre-mersenne.org/articles/10.5802/aif.3162/
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