Szego kernels, Toeplitz operators, and equivariant fixed point formulae
| dc.creator | Paoletti, Roberto | |
| dc.date | 2007-07-10 | |
| dc.date | 2008-03-14 | |
| dc.date.accessioned | 2026-07-07T09:26:29Z | |
| dc.date.available | 2026-07-07T09:26:29Z | |
| dc.description | Let $γ$ be an automorphism of a polarized complex projective manifold $(M,L)$. Then $γ$ induces an automorphism $γ_k$ of the space of global holomorphic sections of the $k$-th tensor power of $L$, for every $k=1,2,...$; for $k\gg 0$, the Lefschetz fixed point formula expresses the trace of $γ_k$ in terms of fixed point data. More generally, one may consider the composition of $γ_k$ with the Toeplitz operator associated to some smooth function on $M$. Still more generally, in the presence of the compatible action of a compact and connected Lie group preserving $(M,L,γ)$, one may consider induced linear maps on the equivariant summands associated to the irreducible representations of $G$. In this paper, under familiar assumptions in the theory of symplectic reductions, we show that the traces of these maps admit an asymptotic expansion as $k\to +\infty$, and compute its leading term. | |
| dc.description | statement and proof simplified, exposition improved, references added | |
| dc.identifier | https://arxiv.org/abs/0707.1375 | |
| dc.identifier | http://arxiv.org/abs/0707.1375 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156767 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | Symplectic Geometry | |
| dc.title | Szego kernels, Toeplitz operators, and equivariant fixed point formulae | |
| dc.type | text |