On a conjecture of V archenko

  title={On a conjecture of V archenko},
  author={Roberto Silvotti},
  journal={Inventiones mathematicae},
  • R. Silvotti
  • Published 26 March 1995
  • Mathematics
  • Inventiones mathematicae
In this note we generalize and prove a recent conjecture of Varchenko concerning the number of critical points of a (multivalued) meromorphic function $\phi$ on an algebraic manifold. Under certain conditions, this number turns out to coincide with the Euler characteristic (up to a sign) of the complement of the divisor of $\phi$. A few variants of this basic situation are also discussed. Two independent proofs are given, respectively using Chern classes and Morse theory In its original form… 

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