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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 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
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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
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).
