Degree growth of monomial maps and McMullen's polytope algebra

Details Degree growth of monomial maps and McMullen's polytope algebra Degree growth of monomial maps and McMullen's polytope algebra

2010-11-12

arxiv.org/abs/1011.2854v2

Mathematics

Dynamical Systems

26 pages. Minor modifications

Scientific paper

We compute all dynamical degrees of monomial maps by interpreting them as
mixed volumes of polytopes. By exploiting further the isomorphism between the
polytope algebra of P. McMullen and the universal cohomology of complete toric
varieties, we construct invariant positive cohomology classes when the
dynamical degrees have no resonance.

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