On the L^2-Stokes theorem and Hodge theory for singular algebraic varieties
| dc.creator | Grieser, D. | |
| dc.creator | Lesch, M. | |
| dc.date | 1999-02-09 | |
| dc.date | 2002-05-07 | |
| dc.date.accessioned | 2026-07-07T06:21:28Z | |
| dc.date.available | 2026-07-07T06:21:28Z | |
| dc.description | For a projective algebraic variety $V$ with isolated singularities, endowed with a metric induced from an embedding, we consider the analysis of the natural partial differential operators on the regular part of $V$. We show that, in the complex case, the Laplacians of the de Rham and Dolbeault complexes are discrete operators except possibly in degrees $n,n\pm 1$, where $n$ is the complex dimension of $V$. We also prove a Hodge theorem on the operator level and the $L^2$--Stokes theorem outside the degrees $n-1,n$. We show that the $L^2$-Stokes theorem may fail to hold in the case of real algebraic varieties, and also discuss the $L^2$-Stokes theorem on more general non-compact spaces. | |
| dc.description | 17 pages; revised version; to appear in Math. Nachrichten | |
| dc.identifier | https://arxiv.org/abs/math/9902062 | |
| dc.identifier | http://arxiv.org/abs/math/9902062 | |
| dc.identifier | Math. Nachr. 246/247 (2002), 68--82 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95611 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 58A (Primary), 32S (Secondary) | |
| dc.title | On the L^2-Stokes theorem and Hodge theory for singular algebraic varieties | |
| dc.type | text |