Equivariant Lefschetz number of differential operators. (English) Zbl 1205.32020
Authors’ abstract: Let \(G\) be a compact Lie group acting on a compact complex manifold \(M\) by holomorphic transformations. We prove a trace density formula for the \(G\)-Lefschetz number of a holomorphic differential operator on \(M\). We generalize the recent results of M. Engeli and the first author [Ann. Sci. Éc. Norm. Supér. (4) 41, No. 4, 623–655 (2008; Zbl 1163.32009)] to orbifolds.
Reviewer: Witold Mozgawa (Lublin)
MSC:
32L99 | Holomorphic fiber spaces |
32W50 | Other partial differential equations of complex analysis in several variables |
58J35 | Heat and other parabolic equation methods for PDEs on manifolds |
16E40 | (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) |
32C38 | Sheaves of differential operators and their modules, \(D\)-modules |
19L10 | Riemann-Roch theorems, Chern characters |
53C55 | Global differential geometry of Hermitian and Kählerian manifolds |
Keywords:
trace of a differential operator; Lefschetz number formula; Riemann–Roch–Hirzebruch formula; \(G\)-invariant differential operator; orbifoldCitations:
Zbl 1163.32009References:
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