19 citations · 81 across the 18 of their papers we have counts for
17 papers · 1 filter
Triangular curves and cyclotomic Zariski tuples
Enrique Artal Bartolo, Jose I. Cogolludo-Agustin, Jorge Martín-Morales
The purpose of this paper is to exhibit infinite families of conjugate projective curves in a number field whose complement have the same abelian fundamental group, but are non-hom…
Wirtinger curves, Artin groups, and hypocycloids
Enrique Artal Bartolo, José Ignacio Cogolludo-Agustín, Jorge Martín-Morales
The computation of the fundamental group of the complement of an algebraic plane curve has been theoretically solved since Zariski-van Kampen, but actual computations are usually c…
Albanese varieties of cyclic covers of the projective plane and orbifold pencils
E. Artal-Bartolo, J. I. Cogolludo-Agustin, A. Libgober
The paper studies a relation between fundamental group of the complement to a plane singular curve and the orbifold pencils containing it. The main tool is the use of Albanese vari…
An arithmetic Zariski pair of line arrangements with non-isomorphic fundamental group
E. Artal, J. I. Cogolludo-Agustín, B. Guerville-Ballé +1
In a previous work, the third named author found a combinatorics of line arrangements whose realizations live in the cyclotomic group of the fifth roots of unity and such that thei…
Numerical Adjunction Formulas for Weighted Projective Planes and Lattice Points Counting
J. I. Cogolludo-Agustin, J. Martin-Morales, J. Ortigas-Galindo
This paper gives an explicit formula for the Ehrhart quasi-polynomial of certain 2-dimensional polyhedra in terms of invariants of surface quotient singularities. Also, a formula f…
The space of curvettes of quotient singularities and associated invariants
Jose I. Cogolludo-Agustin, Jorge Martin-Morales
This paper deals with a complete invariant for cyclic quotient surface singularities. This invariant appears in the Riemann Roch and Numerical Adjunction Formulas for normal…
Arrangements of hypersurfaces and Bestvina-Brady groups
Enrique Artal Bartolo, Jose Ignacio Cogolludo-Agustin, Daniel Matei
We show that quasi-projective Bestvina-Brady groups are fundamental groups of complements to hyperplane arrangements. Furthermore we relate other normal subgroups of right-angled A…
Local invariants on quotient singularities and a genus formula for weighted plane curves
Jose Ignacio Cogolludo-Agustin, Jorge Martin-Morales, Jorge Ortigas-Galindo
In this paper we extend the concept of Milnor fiber and Milnor number of a curve singularity allowing the ambient space to be a quotient surface singularity. A generalization of th…
Kummer covers and braid monodromy
Enrique Artal Bartolo, Jose I. Cogolludo-Agustin, Jorge Ortigas-Galindo
In this work we describe a method to reconstruct the braid monodromy of the preimage of a curve by a Kummer cover. This method is interesting, since it combines two techniques, nam…
Depth of cohomology support loci for quasi-projective varieties via orbifold pencils
E. Artal Bartolo, J. I. Cogolludo-Agustin, A. Libgober
The present paper describes a relation between the quotient of the fundamental group of a smooth quasi-projective variety by its second commutator and the existence of maps to orbi…
Orbifold groups, quasi-projectivity and covers
Enrique Artal Bartolo, Jose Ignacio Cogolludo-Agustin, Daniel Matei
We discuss properties of complex algebraic orbifold groups, their characteristic varieties, and their abelian covers. In particular, we deal with the question of (quasi)-projectivi…
Mordell-Weil groups and Zariski triples
Jose Ignacio Cogolludo-Agustin, Remke Kloosterman
We prove the existence of three irreducible curves of degree 12 with the same number of cusps and different Alexander polynomials. This exhibits a Zariski triple. Moreov…
Depth of characters of curve complements and orbifold pencils
E. Artal Bartolo, J. I. Cogolludo-Agustin, A. Libgober
The present work is a user's guide to the results of a previous paper by the second and third authors, where a description of the space of characters of a quasi-projective variety…
Mordell-Weil groups of elliptic threefolds and the Alexander module of plane curves
J. I. Cogolludo-Agustin, A. Libgober
We show that the degree of the Alexander polynomial of an irreducible plane algebraic curve with nodes and cusps as the only singularities does not exceed where $d…
Quasi-projectivity, Artin-Tits Groups, and Pencil Maps
Enrique Artal Bartolo, Jose Ignacio Cogolludo-Agustin, Daniel Matei
We consider the problem of deciding if a group is the fundamental group of a smooth connected complex quasi-projective (or projective) variety using Alexander-based invariants. In…
Characteristic varieties of quasi-projective manifolds and orbifolds
Enrique Artal Bartolo, Jose Ignacio Cogolludo-Agustin, Daniel Matei
We prove that the irreducible components of the characteristic varieties of quasi-projective manifolds are either pull-backs of such components for orbifolds, or torsion points. Th…
Cohomology algebra of plane curves, weak combinatorial type, and formality
J. I. Cogolludo-Agustin, D. Matei
We determine an explicit presentation by generators and relations of the cohomology algebra of the complement to an algebraic curve in t…