Abstract
We give a new proof of the vanishing of H1(X, V) for negative vector bundles V on normal projective varieties X satisfying rank V < dim X. Our proof is geometric, it uses a topological characterization of the affine bundles associated with nontrivial cocycles α ∈ H1 (X, V) of negative vector bundles. Following the same circle of ideas, we use the analytic characteristics of affine bundles to obtain convexity properties of coverings of projective varieties. We suggest a weakened version of the Shafarevich conjecture: the universal covering X̄ of a projective manifold X is holomorphically convex modulo the pre-image ρ-1(Z) of a subvariety Z ⊂ X. We prove this conjecture for projective varieties X whose pullback map ρ* identifies a nontrivial extension of a negative vector bundle V by script O sign with the trivial extension.
Original language | English (US) |
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Pages (from-to) | 207-222 |
Number of pages | 16 |
Journal | Journal of Algebraic Geometry |
Volume | 15 |
Issue number | 2 |
DOIs | |
State | Published - Apr 2006 |
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology