Combinatorics of Cremona monomial maps

Details Combinatorics of Cremona monomial maps Combinatorics of Cremona monomial maps

2009-04-26

arxiv.org/abs/0904.4065v2

Math. Comp. 81 (2012), no. 279, 1857--1867

Mathematics

Algebraic Geometry

Mathematics of Computation, to appear

Scientific paper

One studies Cremona monomial maps by combinatorial means. Among the results is a simple integer matrix theoretic proof that the inverse of a Cremona monomial map is also defined by monomials of fixed degree, and moreover, the set of monomials defining the inverse can be obtained explicitly in terms of the initial data. A neat consequence is drawn for the plane Cremona monomial group, in particular the known result saying that a plane Cremona (monomial) map and its inverse have the same degree. Included is a discussion about the computational side and/or implementation of the combinatorial invariants stemming from these questions.

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