29 citations · 45 across the 7 of their papers we have counts for
9 papers
Finiteness results concerning algebraic power series
Fuensanta Aroca, Julie Decaup, Guillaume Rond
We construct an explicit filtration of the ring of algebraic power series by finite dimensional constructible sets, measuring the complexity of these series. As an application, we…
The minimal cone of an algebraic Laurent series
Fuensanta Aroca, Julie Decaup, Guillaume Rond
We study the algebraic closure of , the field of power series in several indeterminates over a field . In characteristic zero we show that the elemen…
On Archimedean Zeta Functions and Newton Polyhedra
Fuensanta Aroca, Mirna Gómez-Morales, Edwin León-Cardenal
Let be a polynomial function over the complex numbers and let be a smooth function over with compact support. When is non-degenerate with respect to its Ne…
Support of Laurent series algebraic over the field of formal power series
Fuensanta Aroca, Guillaume Rond
This work is devoted to the study of the support of a Laurent series in several variables which is algebraic over the ring of power series over a characteristic zero field. Our fir…
Puiseux Parametric Equations via the Amoeba of the Discriminant
Fuensanta Aroca, Víctor Manuel Saavedra
Given an algebraic variety we get Puiseux type parametrizations on suitable Reinhardt domains. These domains are defined using the amoeba of hypersurfaces containing the discrimina…
The Fundamental Theorem of Tropical Differential Algebraic Geometry
Fuensanta Aroca, Cristhian Garay, Zeinab Toghani
Let be an ideal of the ring of Laurent polynomials with coefficients in a real-valued field . The fundamental theorem of tropical algeb…
Torical Modification of Newton non-degenerate ideals
Fuensanta Aroca, Mirna Gómez-Morales, Khurram Shabbir
We give a definition of Newton non degeneracy independent of the system of generators defining the variety. This definition extends the notion of Newton non degeneracy to varieties…
Krull-tropical hypersurfaces
Fuensanta Aroca
The concepts of tropical-semiring and tropical hypersurface, are extended for an arbitrary ordered group. Then, we define the tropicalization of a polynomial with coefficients in a…
Puiseux power series solutions for systems of equations
Fuensanta Aroca, Giovanna Ilardi, Lucia Lopez de Medrano
We give an algorithm to compute term by term multivariate Puiseux series expansions of series arising as local parametrizations of zeroes of systems of algebraic equations at singu…