Réunion d'hiver SMC 2014

Université McMaster, 5 - 8 décembre 2014

Prix Jeffery-Williams et conférence

Newton polyhedra connect algebraic geometry and the theory of singularities to the geometry of convex polyhedra inside the framework of toric geometry. This connection is useful in both directions. On the one hand, explicit answers are given to problems of algebra and the theory of singularities in terms of the geometry of polyhedra. For example according to the Bernstein--Kushnirenko theorem the number of solutions of a generic system of $n$ equations in $(\Bbb C^*)^n$ with fixed Newton polyhedra is equal to the mixed volume of the Newton polyhedra multiplied by $n!$. On the other hand, algebraic theorems of general character (like the Hirzebruch--Riemann--Roch theorem) give significant information about the geometry of polyhedra.