Geodesic
Newton polytopes and irreducible components of complete intersections
Izvestiya. Mathematics , Tome 80 (2016) no. 1, pp. 263-284.

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We calculate the number of irreducible components of varieties in $(\mathbb C^*)^n$ determined by generic systems of equations with given Newton polytopes. Every such component can in its turn be given by a generic system of equations whose Newton polytopes are found explicitly. It is known that many discrete invariants of a variety can be found in terms of the Newton polytopes. Our results enable one to calculate such invariants for each irreducible component of the variety.
Keywords: Newton polytopes, mixed volume, irreducible components, holomorphic forms. 
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A. G. Khovanskii. Newton polytopes and irreducible components of complete intersections. Izvestiya. Mathematics , Tome 80 (2016) no. 1, pp. 263-284. http://geodesic.mathdoc.fr/item/IM2_2016_80_1_a8/

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