Algebraic geometry/Differential geometry
Residue formula for Morita–Futaki–Bott invariant on orbifolds
Comptes Rendus. Mathématique, Volume 354 (2016) no. 11, pp. 1109-1113.

In this work, we prove a residue formula for the Morita–Futaki–Bott invariant with respect to any holomorphic vector field, with isolated (possibly degenerated) singularities in terms of Grothendieck's residues.

On obtient, en utilisant les résidus de Grothendieck, une formule résiduelle pour l'invariant de Morita–Futaki–Bott par rapport à un champ de vecteurs holomorphes avec singularités isolées, dégénérées ou non.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.10.006
Corrêa, Maurício 1; Rodríguez, Miguel 2

1 Dep. Matemática ICEx, UFMG, Campus Pampulha, 31270-901 Belo Horizonte, Brazil
2 Dep. Matemática, UFSJ, Praça Frei Orlando, 170, Centro, 36307-352 São João Del Rei, MG, Brazil
@article{CRMATH_2016__354_11_1109_0,
     author = {Corr\^ea, Maur{\'\i}cio and Rodr{\'\i}guez, Miguel},
     title = {Residue formula for {Morita{\textendash}Futaki{\textendash}Bott} invariant on orbifolds},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1109--1113},
     publisher = {Elsevier},
     volume = {354},
     number = {11},
     year = {2016},
     doi = {10.1016/j.crma.2016.10.006},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2016.10.006/}
}
TY  - JOUR
AU  - Corrêa, Maurício
AU  - Rodríguez, Miguel
TI  - Residue formula for Morita–Futaki–Bott invariant on orbifolds
JO  - Comptes Rendus. Mathématique
PY  - 2016
SP  - 1109
EP  - 1113
VL  - 354
IS  - 11
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2016.10.006/
DO  - 10.1016/j.crma.2016.10.006
LA  - en
ID  - CRMATH_2016__354_11_1109_0
ER  - 
%0 Journal Article
%A Corrêa, Maurício
%A Rodríguez, Miguel
%T Residue formula for Morita–Futaki–Bott invariant on orbifolds
%J Comptes Rendus. Mathématique
%D 2016
%P 1109-1113
%V 354
%N 11
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2016.10.006/
%R 10.1016/j.crma.2016.10.006
%G en
%F CRMATH_2016__354_11_1109_0
Corrêa, Maurício; Rodríguez, Miguel. Residue formula for Morita–Futaki–Bott invariant on orbifolds. Comptes Rendus. Mathématique, Volume 354 (2016) no. 11, pp. 1109-1113. doi : 10.1016/j.crma.2016.10.006. http://www.numdam.org/articles/10.1016/j.crma.2016.10.006/

[1] Adem, A.; Leida, J.; Ruan, Y. Orbifolds and String Topology, Cambridge University Press, Cambridge, UK, 2007 (ISBN: 0-511-28288-5)

[2] Bott, R. Vector fields and characteristic numbers, Mich. Math. J., Volume 14 (1967), pp. 231-244

[3] Chern, S.S., Springer-Verlag, New York (1978), pp. 435-443 (Selected Papers)

[4] Ding, W.; Tian, G. Kähler–Einstein metrics and the generalized Futaki invariant, Invent. Math., Volume 110 (1992), pp. 315-335

[5] Futaki, A. An obstruction to the existence of Einstein Kähler metrics, Invent. Math., Volume 73 (1983), pp. 437-443

[6] Futaki, A.; Morita, S. Invariant polynomials on compact complex manifolds, Proc. Jpn. Acad., Ser. A, Math. Sci., Volume 60 (1984) no. 10, pp. 369-372

[7] Futaki, A.; Morita, S. Invariant polynomials of the automorphism group of a compact complex manifold, J. Differ. Geom., Volume 21 (1985), pp. 135-142

[8] Griffiths, P.; Harris, J. Principles of Algebraic Geometry, Wiley, 1978

[9] Li, H.; Shi, Y. The Futaki invariant on the blowup of Kähler surfaces, Int. Math. Res. Not., Volume 2015 (2015) no. 7, pp. 1902-1923 | DOI

[10] Mann, É. Cohomologie quantique orbifolde des espaces projectifs à poids, J. Algebraic Geom., Volume 17 (2008), pp. 137-166

[11] Norguet, F. Fonctions de plusieurs variables complexes, Lect. Notes Math., Volume 409 (1974), pp. 1-97

[12] Viaclovsky, J.A. Einstein metrics and Yamabe invariants of weighted projective spaces, Tohoku Math. J. (2), Volume 65 (2013) no. 2, pp. 297-311

Cited by Sources:

This work was partially supported by CNPq, CAPES, FAPEMIG and FAPESP-2015/20841-5.