

Iskovskikh Seminar
January 23, 2014 18:00, Moscow, Steklov Mathematical Institute, room 540






The Pukhlikov–Khovanskii theorem
E. Yu. Smirnov^{} ^{} National Research University "Higher School of Economics"

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Abstract:
Theorem of Kushnirenko and D.Bernstein on the number of solutions of a system of Laurent polynomial equations in terms of the volumes of their Newton polytopes can be interpreted as a formula for the intersection numbers of divisors in a projecive toric variety. In 1992 Pukhlikov and Khovanskii observed that the Kushnirenko theorem completely determines the cohomology ring of a smooth projective toric variety. I will speak about the PukhlikovKhovanskii theorem and, time permitting, will mention its further generalization to the case of spherical varieties, due to K.Kaveh.

