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

Newstead, P. E.

doi:10.1090/S0002-9947-1972-0316452-9

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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