Geometry of Deligne cohomology

Details Geometry of Deligne cohomology Geometry of Deligne cohomology

1996-01-26

arxiv.org/abs/alg-geom/9601025v1

Mathematics

Algebraic Geometry

51 pages, uses XY-pic, author-supplied PostScript and DVI files available at http://www.math.tamu.edu/~pawel.gajer/gdc.html .

Scientific paper

10.1007/s002220050118

It is well known that degree two Deligne cohomology groups can be identified with groups of isomorphism classes of holomorphic line bundles with connections. There is also a geometric description of degree three Deligne cohomology, due to J-L. Brylinski and P. Deligne, in terms of gerbes with connective structures and curvings. This paper gives a geometric interpretation of Deligne cohomology of all degrees, in terms of equivalence classes of higher line bundles with $k$-connections. It is also shown that the classical Abel-Jacobi isomorphism $Pic^0(X) \cong J(X)$ generalizes to the isomorphism between groups of equivalence classes of topologically trivial 1-holomorphic higher line bundles with $k$-connections and Griffiths intermediate Jacobians.

Affiliated with

Also associated with

No associations

Rating

Geometry of Deligne 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 Geometry of Deligne cohomology, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometry of Deligne cohomology will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-508763