# On a conjecture of V archenko

@article{Silvotti1996OnAC, title={On a conjecture of V archenko}, author={Roberto Silvotti}, journal={Inventiones mathematicae}, year={1996}, volume={126}, pages={235-248} }

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
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