Secondary Kodaira-Spencer classes and nonabelian Dolbeault cohomology
| dc.creator | Simpson, Carlos | |
| dc.date | 1997-12-18 | |
| dc.date | 1998-01-06 | |
| dc.date.accessioned | 2026-07-07T01:51:25Z | |
| dc.date.available | 2026-07-07T01:51:25Z | |
| dc.description | If $X$ is a smooth projective variety moving in a family, we define a secondary Kodaira-Spencer class for nonabelian Dolbeault cohomology $Hom(X_{Dol}, T)$ of $X$ with coefficients in the complexified 2-sphere $T=S^2\otimes \cc$ (which is a 3-stack on $Sch /\cc$). Let $Z$ be a simply connected projective surface with $h^{2,0}\neq 0$, and let $X$ be the blow-up of $Z$ at a point $P$. As $P$ moves in $Z$, the blow-up $X$ moves in a family and we show that the secondary Kodaira-Spencer class is nontrivial. This contrasts with the fact that the variations of mixed Hodge structures on the homotopy groups of $X$ are constant. We discuss various surrounding notions, including two appendices where we give some details about the Breen calculations in characteristic zero and representability of simply connected complex shapes. | |
| dc.description | 75 pages. Correction-existence and functoriality of decomposition of an infinite loop stack into product of Eilenberg-MacLane stacks don't hold in general. However, what we need for the calculation is still true | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9712020 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9712020 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/293 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Secondary Kodaira-Spencer classes and nonabelian Dolbeault cohomology | |
| dc.type | text |