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Fibers of multi-graded rational maps and orthogonal projection onto rational surfaces
(Society for Industrial and Applied Mathematics, 2020-06)
We contribute a new algebraic method for computing the orthogonal projections of a point onto a rational algebraic surface embedded in the three-dimensional projective space. This problem is first turned into the computation ...
On the minimal field of definition of rational maps: Rational maps of odd signature
(2018)
The field of moduli of a rational map is an invariant under conjugation by Mobius transformations. Silverman proved that a rational map, either of even degree or equivalent to a polynomial, is definable over its field of ...
Thermodynamic formalism of rational maps
(2016)
About 20 years ago, Makarov and Smirnov started
their study of the thermodynamic formalism of rational maps
and its connection to the integral means spectrum. For an
arbitrary rational map, they gave a complete characterization
of ...
Compactifications of rational maps, and the implicit equations of their images
(Elsevier Science, 2010-05)
In this paper, we give different compactifications for the domain and the codomain of an affine rational map f which parameterizes a hypersurface. We show that the closure of the image of this map (with possibly some other ...