Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces

Details Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces

2000-06-24

arxiv.org/abs/math/0006186v2

Mathematics

Differential Geometry

113 pages, 6 figures, latex2e with packages hyperref, amsart, graphicx. For Version 2: Many typos corrected, important referen

Scientific paper

I use local differential geometric techniques to prove that the algebraic cycles in certain extremal homology classes in Hermitian symmetric spaces are either rigid (i.e., deformable only by ambient motions) or quasi-rigid (roughly speaking, foliated by rigid subvarieties in a nontrivial way). These rigidity results have a number of applications: First, they prove that many subvarieties in Grassmannians and other Hermitian symmetric spaces cannot be smoothed (i.e., are not homologous to a smooth subvariety). Second, they provide characterizations of holomorphic bundles over compact Kahler manifolds that are generated by their global sections but that have certain polynomials in their Chern classes vanish (for example, c_2 = 0, c_1c_2 - c_3 = 0, c_3 = 0, etc.).

Affiliated with

Also associated with

No associations

Rating

Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces 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 Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-435984