701 research outputs found
Cartier and Weil Divisors on Varieties with Quotient Singularities
The main goal of this paper is to show that the notions of Weil and Cartier
-divisors coincide for -manifolds and give a procedure to
express a rational Weil divisor as a rational Cartier divisor. The theory is
illustrated on weighted projective spaces and weighted blow-ups.Comment: 16 page
Superisolated Surface Singularities
In this survey, we review part of the theory of superisolated surface
singularities (SIS) and its applications including some new and recent
developments. The class of SIS singularities is, in some sense, the simplest
class of germs of normal surface singularities. Namely, their tangent cones are
reduced curves and the geometry and topology of the SIS singularities can be
deduced from them. Thus this class \emph{contains}, in a canonical way, all the
complex projective plane curve theory, which gives a series of nice examples
and counterexamples. They were introduced by I. Luengo to show the
non-smoothness of the -constant stratum and have been used to answer
negatively some other interesting open questions. We review them and the new
results on normal surface singularities whose link are rational homology
spheres. We also discuss some positive results which have been proved for SIS
singularities.Comment: Survey article for the Proceedings of the Conference "Singularities
and Computer Algebra" on Occasion of Gert-Martin Greuel's 60th Birthday, LMS
Lecture Notes (to appear
Pencils and Infinite Dihedral covers of P^2
In this work we study the connection between the existence of finite dihedral
covers of the projective plane ramified along an algebraic curve C, infinite
dihedral covers, and pencils of curves containing C.Comment: 1o page
Depth of cohomology support loci for quasi-projective varieties via orbifold pencils
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 orbifold curves. It extends previously studied
cases when the target was a smooth curve. In the case when the quasi-projective
variety is a complement to a plane algebraic curve this provides new relations
between the fundamental group, the equation of the curve, and the existence of
polynomial solutions to certain equations generalizing Pell's equation. These
relations are formulated in terms of the depth which is an invariant of the
characters of the fundamental group discussed in detail here.Comment: 22 page
Characteristic varieties of graph manifolds and quasi-projectivity of fundamental groups of algebraic links
The present paper studies the structure of characteristic varieties of
fundamental groups of graph manifolds. As a consequence, a simple proof of
Papadima's question is provided on the characterization of algebraic links that
have quasi-projective fundamental groups. The type of quasi-projective
obstructions used here are in the spirit of Papadima's original work.Comment: 22 pages, 6 figures, to appear in European Journal of Mathematic
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