# 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}
}
• 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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