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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Characteristic classes of stable bundles of rank $2$ over an algebraic curve
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by P. E. Newstead PDF
Trans. Amer. Math. Soc. 169 (1972), 337-345 Request permission

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
  • © Copyright 1972 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 169 (1972), 337-345
  • MSC: Primary 14D20; Secondary 14F05
  • DOI: https://doi.org/10.1090/S0002-9947-1972-0316452-9
  • MathSciNet review: 0316452