An explicit proof of the generalized Gauss-Bonnet formula
From probability to geometry (II) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 328 (2009), pp. 137-160. 
@incollection{AST_2009__328__137_0,
     author = {Gillet, Henri and \"Unl\"u, Fatih M.},
     title = {An explicit proof of the generalized {Gauss-Bonnet} formula},
     booktitle = {From probability to geometry (II) - Volume in honor of the 60th birthday of Jean-Michel Bismut},
     editor = {Dai Xianzhe and L\'eandre R\'emi and Xiaonan Ma and Zhang Weiping},
     series = {Ast\'erisque},
     pages = {137--160},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {328},
     year = {2009},
     mrnumber = {2664468},
     zbl = {1235.32006},
     language = {en},
     url = {http://archive.numdam.org/item/AST_2009__328__137_0/}
}
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Gillet, Henri; Ünlü, Fatih M. An explicit proof of the generalized Gauss-Bonnet formula, dans From probability to geometry (II) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 328 (2009), pp. 137-160. http://archive.numdam.org/item/AST_2009__328__137_0/

[1] A. Altman & S. Kleiman - Introduction to Grothendieck duality theory, Lecture Notes in Math., vol. 146, Springer, 1970. | MR | Zbl

[2] M. F. Atiyah - "Complex analytic connections in fibre bundles", Trans. Amer. Math. Soc. 85 (1957), p. 181-207. | DOI | MR | Zbl

[3] M. F. Atiyah & F. Hirzebruch - "Analytic cycles on complex manifolds", Topology 1 (1962), p. 25-45. | DOI | MR | Zbl

[4] N. Berline, E. Getzler & M. Vergne - Heat kernels and Dirac operators, Grund. Math. Wiss., vol. 298, Springer, 1992. | MR | Zbl

[5] E. H. J. Brown - "Twisted tensor products. I", Ann. of Math. 69 (1959), p. 223-246. | DOI | MR | Zbl

[6] P. Dolbeault - "Formes différentielles et cohomologie sur une variété analytique complexe. I", Ann. of Math. 64 (1956), p. 83-130. | DOI | MR | Zbl

[7] G. Fischer - Complex analytic geometry, Lecture Notes in Math., vol. 538, Springer, 1976. | MR | Zbl

[8] P. Griffiths & J. Harris - Principles of algebraic geometry, Wiley Classics Library, John Wiley & Sons Inc., 1994. | DOI | MR | Zbl

[9] A. Grothendieck - "Théorèmes de dualité pour les faisceaux algébriques cohérents", in Séminaire Bourbaki, Vol. 4, exp. n° 149, Soc. Math. France, 1995, p. 169-193. | EuDML | Numdam | MR | Zbl

[10] M. Kapranov - "Rozansky-Witten invariants via Atiyah classes", Compositio Math. 115 (1999), p. 71-113. | DOI | MR | Zbl

[11] D. Quillen - "Superconnections and the Chern character", Topology 24 (1985), p. 89-95. | DOI | MR | Zbl

[12] D. Toledo & Y. L. L. Tong - "The holomorphic Lefschetz formula", Bull Amer. Math. Soc. 81 (1975), p. 1133-1135. | DOI | MR | Zbl

[13] D. Toledo & Y. L. L. Tong, "A parametrix for ∂ ¯ and Riemann-Roch in Cech theory", Topology 15 (1976), p. 273-301. | DOI | MR | Zbl

[14] D. Toledo & Y. L. L. Tong, "Duality and intersection theory in complex manifolds. I", Math. Ann. 237 (1978), p. 41-77. | DOI | EuDML | MR | Zbl