Characteristic classes of stable bundles of rank 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 be a complete nonsingular algebraic curve over and a line bundle of degree 1 over . It is well known that the isomorphism classes of stable bundles of rank 2 and determinant over form a nonsingular projective variety . The Betti numbers of are also known. In this paper we define certain distinguished cohomology classes of and prove that these classes generate the rational cohomology ring. We also obtain expressions for the Chern character and Pontrjagin classes of in terms of these generators.

**[1]**D. Mumford and P. Newstead,*Periods of a moduli space of bundles on curves*, Amer. J. Math.**90**(1968), 1200–1208. MR**0234958****[2]**M. S. Narasimhan and C. S. Seshadri,*Stable and unitary vector bundles on a compact Riemann surface*, Ann. of Math. (2)**82**(1965), 540–567. MR**0184252****[3]**P. E. Newstead,*Topological properties of some spaces of stable bundles*, Topology**6**(1967), 241–262. MR**0232015****[4]**P. E. Newstead,*Stable bundles of rank 2 and odd degree over a curve of genus 2*, Topology**7**(1968), 205–215. MR**0237500****[5]**S. Ramanan,*Holomorphic vector bundles on homogeneous spaces*, Topology**5**(1966), 159–177. MR**0190947****[6]**C. S. Seshadri,*Moduli of -vector bundles over an algebraic curve*, Lectures at the Summer Institute, Varenna, 1969.

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DOI:
https://doi.org/10.1090/S0002-9947-1972-0316452-9

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