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Artal Bartolo, Enrique ; Carmona Ruber, Jorge ; Cogolludo Agustín, José Ignacio | DUKE UNIV PRESS | 2003In this paper we prove that braid monodromy of an affine plane curve determines the topology of a related projective plane curve.texto impreso
Artal Bartolo, Enrique ; Carmona Ruber, Jorge ; Cogolludo Agustín, José Ignacio | American Mathematical Society | 2007In this paper we construct new invariants of algebraic curves based on (not necessarily generic) braid monodromies. Such invariants are effective in the sense that their computation allows for the study of Zariski pairs of plane curves. Moreover[...]texto impreso
Artal Bartolo, Enrique ; Carmona Ruber, Jorge ; Cogolludo Austín, José Ignacio | Cambridge Philosophical Society | 2004We give an algebraic and topological interpretation of essential coordinate components of characteristic varieties and illustrate their importance with an example.texto impreso
Escribano Martínez, Jesús ; Carmona Ruber, Jorge ; Valdés Morales, Antonio ; Baro González, Elías ; Caravantes Tortajada, Jorge ; Claramunt Pérez, Juan Andrés ; Fernández Rodríguez, María Pilar ; Bellido Terrones, María Luz Divina | 2017-06-30Difusión, entre los estudiantes y los profesores de la Facultad de Matemáticas de la UCM, de herramientas de software libre en las labores académica. En particular, abogamos por el uso de SAGE (www.sagemath.org).texto impreso
Artal Bartolo, Enrique ; Carmona Ruber, Jorge ; Cogolludo Agustín, José Ignacio ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro | Editorial Complutense | 2000The article under review contains a study of the topology of a pair (P2,C), where C is an algebraic curve in the complex projective plane. The basic problem is to find invariants which are sensitive enough to distinguish many pairs, and for whic[...]texto impreso
Artal Bartolo, Enrique ; Carmona Ruber, Jorge ; Cogolludo Agustín, José Ignacio ; Marco Buzunáriz, Miguel ángel | Mathematical Society of Japan | 2006Following the general strategy proposed by G.Rybnikov, we present a proof of his well-known result, that is, the existence of two arrangements of lines having the same combinatorial type, but nonisomorphic fundamental groups. To do so, the Alexa[...]texto impreso
Artal Bartolo, Enrique ; Carmona Ruber, Jorge ; Melle Hernández, Alejandro | Cambridge University Press | 2010This note provides a negative answer to the following question of A. H. Durfee [Invent. Math. 28 (1975), 231–241; ]: Is it true for arbitrary polynomials F(x,y,z) having an isolated singularity at the origin that the local monodromy is of finite[...]texto impreso
Artal Bartolo, Enrique ; Carmona Ruber, Jorge ; Cogolludo Agustín, José Ignacio | Birkhäuser Basel | 2002In this work we present an exhaustive description, up to projective isomorphism, of all irreducible sextic curves in ?2 having a singular point of type , A n ,n?15 n ? 15, only rational singularities and global Milnor number at least 18. Moreov[...]texto impreso
Carmona Ruber, Jorge ; Artal, E. ; Cogolludo, J.I. ; Tokunaga, H.O. | World Scientific PublCo | 2001is the first example of this kind known. The two curves of the pair have a trivial Alexander polynomial. The difference in the topology of their complements can only be detected via finer invariants or techniques. In our case the generic braid m[...]texto impreso
Artal Bartolo, Enrique ; Carmona Ruber, Jorge ; Cogolludo Agustín, José Ignacio ; Escario Gil, Mario ; Fernández de Bobadilla de Olarzábal, Javier José ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro | Editorial Complutense | 2004We study properties of arrangements of rational plane curves. The existence of such curves with prescribed topological data has a lot of geometric restrictions. We show how to use the theory of singular complex analytic spaces to obtain such res[...]texto impreso
Artal Bartolo, Enrique ; Carmona Ruber, Jorge ; Cogolludo Agustín, José Ignacio ; Marcos Buzunáriz, Miguel Ángel | Cambridge University Press | 2005We prove the existence of complexified real arrangements with the same combinatorics but different embeddings in P2. Such a pair of arrangements has an additional property: they admit conjugated equations on the ring of polynomials over Q(?5).texto impreso
