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Listar por autor "Galindo Pastor, Carlos"

Mostrando ítems 1-10 de 10

A class of polynomial planar vector fields with polynomial first integral

Ferragut, Antoni; Galindo Pastor, Carlos; Monserrat Delpalillo, Francisco José (Elsevier, 2015-10-01)

We give an algorithm for deciding whether a planar polynomial differential system has a first integral which factorizes as a product of defining polynomials of curves with only one place at infinity. In the affirmative ...
Evaluation codes defined by finite families of plane valuations at infinity

Galindo Pastor, Carlos; Monserrat Delpalillo, Francisco José (Springer Verlag (Germany), 2014-01)

We construct evaluation codes given by weight functions defined over polynomial rings in m a parts per thousand yen 2 indeterminates. These weight functions are determined by sets of m-1 weight functions over polynomial ...
Finite families of plane valuations: value semigroup, graded algebra and Poincaré series

Monserrat Delpalillo, Francisco José; Galindo Pastor, Carlos (American Mathematical Society, 2012)

[EN] In this paper, the authors are interested in some applications of valuation theory to algebraic geometry and, particularly, to singularity theory. The aim of this paper is to provide a concise survey of some aspects ...
Foliations with isolated singularities on Hirzebruch surfaces

Galindo Pastor, Carlos; Monserrat Delpalillo, Francisco José; Olivares, Jorge (Walter de Gruyter GmbH, 2021-10-10)

[EN] We study foliations F on Hirzebruch surfaces Sd and prove that, similarly to those on the projective plane, any F can be represented by a bi-homogeneous polynomial affine 1-form. In case F has isolated singularities, ...
Minimal plane valuations

Galindo Pastor, Carlos; Monserrat Delpalillo, Francisco José; Moyano-Fernández, J.J. (American Mathematical Society, 2018-07-16)

[EN] We consider the value (mu) over cap(nu) = lim(m -> infinity) m(-1) a(mL), where a(mL) is the last value of the vanishing sequence of H-0(mL) along a divisorial or irrational valuation nu centered at O-P2,(p), L ...
On the computation of Darboux first integrals of a class of planar polynomial vector fields

Ferragut, Antoni; GALINDO PASTOR, CARLOS; Monserrat Delpalillo, Francisco José (Elsevier, 2019-10-15)

[EN] We study the class of planar polynomial vector fields admitting Darboux first integrals of the type Pi(r)(i=1) f(i)(alpha i), where the alpha(i)'s are positive real numbers and the f(i)'s are polynomials defining ...
The Abhyankar-Moh theorem for plane valuations at infinity

Galindo Pastor, Carlos; Monserrat Delpalillo, Francisco José (Elsevier, 2013-01-15)

We introduce the class of plane valuations at infinity and prove an analogue to the Abhyankar-Moh (semigroup) Theorem for it. © 2012 Elsevier Inc. All rights reserved.
The cone of curves and the Cox ring of rational surfaces given by divisorial valuations

Galindo Pastor, Carlos; Monserrat Delpalillo, Francisco José (Elsevier, 2016-02-26)

We consider surfaces X defined by plane divisorial valuations v of the quotient field of the local ring R at a closed point p of the projective plane P-2 over an arbitrary algebraically closed field k and centered at R. ...
The log-canonical threshold of a plane curve

Galindo Pastor, Carlos; Hernando, Fernando; Monserrat Delpalillo, Francisco José (Cambridge University Press (CUP), 2016)

We give an explicit formula for the log-canonical threshold of a reduced germ of plane curve. The formula depends only on the first two maximal contact values of the branches and their intersection multiplicities. We also ...
The Poincaré problem, algebraic integrability and dicritical divisors

Galindo Pastor, Carlos; Monserrat Delpalillo, Francisco José (Elsevier, 2014-06-01)

We solve the Poincaré problem for plane foliations with only one dicritical divisor. Moreover, in this case, we give a simple algorithm that decides whether a foliation has a rational first integral and computes it in the ...