MNOGOGRANNIKI NYUTONA I VYCHETY GROTENDIKA

O.A.Gelfond, A.G.Khovanskii

Rassmotrim sistemu  uravnenii $P_1=\dots=P_n=0$ v $(\Bbb C\setminus 0)^n$,
gde $P_1,\dots,P_n$ --- polinomy Lorana s mnogogrannikami Nyutona
$\Delta_1,\dots,\Delta_n$. S kazhdym polinomom Lorana $Q$ svyazhem $n$-formu
$\omega = Q/P\cdot \frac{ dz_1}{z_1}\wedge \dots\wedge \frac{dz_n}{z_n}$,
gde $z_1,\dots z_n$ --- nezavisimye peremennye i $P=P_1\cdot\dots\cdot P_n$.
Dlya obshchikh naborov mnogogrannikov $\Delta_1,\dots,\Delta_n$
vychislyaetsya summa vychetov Grotendika formy $\omega$ po vsem
kornyam sistemy uravnenii.