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Semipositive Bundles and Brill–Noether Theory
Author(s) -
Muñoz Vicente,
Presas Francisco
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609302001741
Subject(s) - mathematics , noether's theorem , vector bundle , pure mathematics , brill , holomorphic function , morphism , complex manifold , homotopy , unipotent , hyperplane , irreducibility , mathematics subject classification , manifold (fluid mechanics) , algebra over a field , combinatorics , lagrangian , mechanical engineering , philosophy , theology , engineering
A Lefschetz hyperplane theorem for the determinantal loci of a morphism between two holomorphic vector bundles E and F over a complex manifold is proved, under the condition that E * ⊗ F is Griffiths k ‐positive. This result is applied to find some homotopy groups of the Brill–Noether loci for a generic curve. 2000 Mathematics Subject Classification 32Q55, 14M12, 14H51.