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math.AG2007★ 1 cited
A refinement of the Kushnirenko-Bernstein estimate
Patrice Philippon, Martin Sombra
A theorem of Kushnirenko and Bernstein shows that the number of isolated roots of a system of polynomials in a torus is bounded above by the mixed volume of the Newton polytopes of…
math.AG2005
Diophantine geometry and toric varieties
Patrice Philippon, Martin Sombra
We present some results on projective toric varieties which are relevant in Diophantine geometry. We interpret and study several invariants attached to these varieties in geometric…