Virtual fundamental classes via dg-manifolds
| dc.creator | Ciocan-Fontanine, Ionut | |
| dc.creator | Kapranov, Mikhail | |
| dc.date | 2007-03-08 | |
| dc.date | 2007-06-26 | |
| dc.date.accessioned | 2026-07-07T08:12:20Z | |
| dc.date.available | 2026-07-07T08:12:20Z | |
| dc.description | We construct virtual fundamental classes for dg-manifolds whose tangent sheaves have cohomology only in degrees 0 and 1. This condition is analogous to the existence of a perfect obstruction theory in the approach of Behrend-Fantechi [BF] or Li-Tian [LT]. Our class is initially defined in K-theory, as the class of the structure sheaf of the dg-manifold. We compare our construction with that of [BF] as well as with the original proposal of Kontsevich. We prove a Riemann-Roch type result for dg-manifolds which involves integration over the virtual class. We prove a localization theorem for our virtual classes. We also associate to any dg-manifold of our type a cobordism class of almost complex (smooth) manifolds. This supports the intuition that working with dg-manifolds is the correct algebro-geometric replacement of the analytic technique of "deforming to transversal intersection". | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/math/0703214 | |
| dc.identifier | http://arxiv.org/abs/math/0703214 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132420 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Virtual fundamental classes via dg-manifolds | |
| dc.type | text |