[115] A Remark on Integral Geometry

  • Raoul Bott
  • Cliff Taubes
Part of the Contemporary Mathematicians book series (CM)


The occasion for this note is the following result of Shub and Smale [SS] on the average number of solutions of polynomial equations over the reals.

Suppose that {f1,…,fn} are nhomogeneous polynomials in(n+1)variables(x0…,xn).Then generically the simultaneous solutions of the equations

$${f_i}\left( x \right)\, = \,0\,,\,\,\,\,\,\,\,\,\,i\, = \,1, \ldots ,n$$


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Authors and Affiliations

  • Raoul Bott
    • 1
  • Cliff Taubes
    • 1
  1. 1.Harvard University, Dept. of MathematicsCambridgeUSA

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