Let C be a smooth projective curve with Jacobian J and let C(n) denote the nth symmetric product of C with itself. For n sufficiently large there is a map C(n) !J that makes C(n) into a projective bundle over J, associated with a certain vector bundleE over J. In an article by A. Mattuck [Amer. J. Math. 83 (1961), 189–206; ], the Chern classes of E were computed in terms of powers of the rational equivalence class of the canonical subvariety of C(n) (isomorphic to C(n−1)). We generalize these computations to a special kind of vector bundle F over a smooth quasi-projective variety. The necessary restriction on F is grosso modo that of having m general sections, for some m < rk F.
A property of a special class of algebraic vector bundles..
COLLINO, Alberto
1976-01-01
Abstract
Let C be a smooth projective curve with Jacobian J and let C(n) denote the nth symmetric product of C with itself. For n sufficiently large there is a map C(n) !J that makes C(n) into a projective bundle over J, associated with a certain vector bundleE over J. In an article by A. Mattuck [Amer. J. Math. 83 (1961), 189–206; ], the Chern classes of E were computed in terms of powers of the rational equivalence class of the canonical subvariety of C(n) (isomorphic to C(n−1)). We generalize these computations to a special kind of vector bundle F over a smooth quasi-projective variety. The necessary restriction on F is grosso modo that of having m general sections, for some m < rk F.
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