Related papers: Obstructions on fundamental groups of plane curve …
We give a complete description of all order 1 invariants of planar curves.
We describe methods for calculation of polytopes of quasiadjunction for plane curve singularities which are invariants giving a Hodge theoretical refinement of the zero sets of multivariable Alexander polynomials. In particular we identify…
This paper studies the obstructions to deforming a map from a complex variety to another variety which is an immersion of codimension one. We extend the classical notion of semiregularity of subvarieties to maps between varieties, and show…
We define an invariant for the existence of r pointwise linearly independent sections in the tangent bundle of a closed manifold. For low values of r, explicit computations of the homotopy groups of certain Thom spectra combined with…
Finite-order invariants of knots in arbitrary 3-manifolds (including non-orientable ones) are constructed and studied by methods of the topology of discriminant sets. Obstructions to the integrability of admissible weight systems to…
The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…
Near a singular point of a surface or a curve, geometric invariants diverge in general, and the orders of diverge, in particular the boundedness about these invariants represent geometry of the surface and the curve. In this paper, we study…
For affine algebraic plane curves we reduce a calculation of its invariants to calculation of the intersection of kernels of some derivations.
Let G be a simple complex algebraic group. By using a notion of a G-category we define invariants of tangles with flat G-connections in their complements. We also show that quantized universal enveloping algebras at roots of unity provide…
We construct two combinatorially equivalent line arrangements in the complex projective plane such that the fundamental groups of their complements are not isomorphic. The proof uses a new invariant of the fundamental group of the…
We introduce a new family of invariants of real algebraic sets defined in terms of the topology of their complexifications and compute some of these invariants for spheres. This allows us to completely classify topological isomorphism…
We classify invariant curves for birational surface maps that are expanding on cohomology. When the expansion is exponential, the arithmetic genus of an invariant curve is at most one. This implies severe constraints on both the type and…
We survey recent developments in the study of Hodge theoretic aspects of Alexander-type invariants associated with smooth complex algebraic varieties.
We start with a discussion on Alexander invariants, and then prove some general results concerning the divisibility of the Alexander polynomials and the supports of the Alexander modules, via Artin's vanishing theorem for perverse sheaves.…
We introduce four invariants of algebraic varieties over imperfect fields, each of which measures either geometric non-normality or geometric non-reducedness. The first objective of this article is to establish fundamental properties of…
We give a short introduction to the theory of twisted Alexander polynomials of a 3--manifold associated to a representation of its fundamental group. We summarize their formal properties and we explain their relationship to twisted…
The fundamental group of the complement of a hyperplane arrangement in a complex vector space is an important topological invariant. The third rank of successive quotients in the lower central series of the fundamental group was called Falk…
This is an introduction to topology of complement to plane curves and hypersurfaces in the projective space and is based on the lectures given in Lumini in February and in ICTP (Trieste) in August of 2005. We discuss key problems concerning…
We characterise, in terms of Dixmier-Ohno invariants, the types of singularities that a plane quartic curve can have. We then use these results to obtain new criteria for determining the stable reduction types of non-hyperelliptic curves of…
In this paper we investigate Uludag's method for constructing new curves whose fundamental groups are central extensions of the fundamental group of the original curve by finite cyclic groups. In the first part, we give some generalizations…