Secondary Kodaira-Spencer classes and nonabelian Dolbeault cohomology

Details Secondary Kodaira-Spencer classes and nonabelian Dolbeault cohomology Secondary Kodaira-Spencer classes and nonabelian Dolbeault cohomology

1997-12-18

arxiv.org/abs/alg-geom/9712020v2

Mathematics

Algebraic Geometry

75 pages. Correction-existence and functoriality of decomposition of an infinite loop stack into product of Eilenberg-MacLane

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Secondary Kodaira-Spencer classes and nonabelian Dolbeault cohomology does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Secondary Kodaira-Spencer classes and nonabelian Dolbeault cohomology, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Secondary Kodaira-Spencer classes and nonabelian Dolbeault cohomology will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-324295