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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Characteristic classes of stable bundles of rank $ 2$ over an algebraic curve


Author: P. E. Newstead
Journal: Trans. Amer. Math. Soc. 169 (1972), 337-345
MSC: Primary 14D20; Secondary 14F05
MathSciNet review: 0316452
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Abstract: Let $ X$ be a complete nonsingular algebraic curve over $ {\mathbf{C}}$ and $ L$ a line bundle of degree 1 over $ X$. It is well known that the isomorphism classes of stable bundles of rank 2 and determinant $ L$ over $ X$ form a nonsingular projective variety $ S(X)$. The Betti numbers of $ S(X)$ are also known. In this paper we define certain distinguished cohomology classes of $ S(X)$ and prove that these classes generate the rational cohomology ring. We also obtain expressions for the Chern character and Pontrjagin classes of $ S(X)$ in terms of these generators.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0316452-9
PII: S 0002-9947(1972)0316452-9
Keywords: Families of stable bundles, moduli spaces, cohomology ring, generators and relations, characteristic classes, Chern classes, Pontrjagin classes
Article copyright: © Copyright 1972 American Mathematical Society