1. Semipositive bundles and Brill-Noether theory
- Author
-
Francisco Presas and Vicente Muñoz
- Subjects
Mathematics - Differential Geometry ,14H51 ,Pure mathematics ,Topología ,Chern class ,General Mathematics ,Bott periodicity theorem ,Lefschetz hyperplane theorem ,Holomorphic function ,Vector bundle ,Algebra ,Mathematics - Algebraic Geometry ,Mathematics::Algebraic Geometry ,Geometria algebraica ,Differential Geometry (math.DG) ,Line bundle ,FOS: Mathematics ,Brill–Noether theory ,14M12 ,Complex manifold ,32Q55 ,Algebraic Geometry (math.AG) ,Mathematics::Symplectic Geometry ,Mathematics - Abstract
We prove a Lefschetz hyperplane theorem for the determinantal loci of a morphism between two holomorphic vector bundles $E$ and $F$ over a complex manifold under the condition that $E^*\ox F$ is Griffiths $k$-positive. We apply this result to find some homotopy groups of the Brill-Noether loci for a generic curve., Comment: (one small mistake corrected)
- Published
- 2003