Hearing the weights of weighted projective planes
| dc.creator | Abreu, Miguel | |
| dc.creator | Dryden, Emily | |
| dc.creator | Freitas, Pedro | |
| dc.creator | Godinho, Leonor | |
| dc.date | 2006-08-18 | |
| dc.date.accessioned | 2026-07-07T07:21:55Z | |
| dc.date.available | 2026-07-07T07:21:55Z | |
| dc.description | Which properties of an orbifold can we ``hear,'' i.e., which topological and geometric properties of an orbifold are determined by its Laplace spectrum? We consider this question for a class of four-dimensional Kähler orbifolds: weighted projective planes $M:=\C P^2(N_1,N_2,N_3)$ with three isolated singularities. We show that the spectra of the Laplacian acting on 0- and 1-forms on $M$ determine the weights $N_1$, $N_2$, and $N_3$. The proof involves analysis of the heat invariants using several techniques, including localization in equivariant cohomology. We show that we can replace knowledge of the spectrum on 1-forms by knowledge of the Euler characteristic and obtain the same result. Finally, after determining the values of $N_1$, $N_2$, and $N_3$, we can hear whether $M$ is endowed with an extremal Kähler metric. | |
| dc.description | 23 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0608462 | |
| dc.identifier | http://arxiv.org/abs/math/0608462 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115471 | |
| dc.subject | Differential Geometry | |
| dc.subject | Spectral Theory | |
| dc.subject | 58J50 (Primary) 53D20; 55N91 (Secondary) | |
| dc.title | Hearing the weights of weighted projective planes | |
| dc.type | text |