2000/06/24 by Robert L. Bryant, Bryant, Robert L. · 3 citations
Mathematics · #14C25 (Primary) 32M15 #57T15 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #math.AG #math.DG #msc:14C25 #msc:32M15 #msc:57T15
paper · pdf · doi:10.48550/arxiv.math/0006186
113 pages, 6 figures, latex2e with packages hyperref, amsart, graphicx. For Version 2: Many typos corrected, important references added (esp. to Maria Walters' thesis), several proofs or statements improved and/or corrected
openalex publication_date 2000/06/24 · arxiv created 2001/03/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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, c2 = 0, c1c2 - c3 = 0, c3 = 0, etc.).