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A note on the connectedness of the branch locus of rational maps
(2018)
Milnor proved that the moduli space M-d of rational maps of degree d >= 2 has a complex orbifold structure of dimension 2(d - 1). Let us denote by S-d the singular locus of M-d and by B-d the branch locus, that is, the ...
Effective criteria for bigraded birational maps
(Academic Press Ltd - Elsevier Science Ltd, 2017-07)
In this paper, we consider rational maps whose source is a product of two subvarieties, each one being embedded in a projective space. Our main objective is to investigate birationality criteria for such maps. First, a ...
Ergodic theory of rational fractions on ultrametric bodies
(WILEY, 2010)
We make the first steps towards an understanding of the ergodic properties of a rational map defined over a complete algebraically closed non-archimedean field. For such a rational map R, we construct a natural invariant ...
Implicitación de aplicaciones racionalesImplicitization of rational maps
(Facultad de Ciencias Exactas y Naturales. Universidad de Buenos Aires, 2010)
Large deviation principles for non-uniformly hyperbolic rational maps
(CAMBRIDGE UNIV PRESS, 2011)
We show some level-2 large deviation principles for rational maps satisfying a strong form of non-uniform hyperbolicity, called 'Topological Collet-Eckmann'. More precisely, we prove a large deviation principle for the ...