Invariants of Combinatorial Line Arrangements and Rybnikov's Example

Following 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 non-isomorphic fundamental groups. To do so, the Alexander Invariant and certain invariants of combinatorial line arrangements are presented and developed for combinatorics with only double and triple points. This is part of a more general project to better understand the relationship between topology and combinatorics of line arrangements.Comment: 27 pages, 2 eps figure

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

Phase-transfer function of the human eye and its influence on point-spread function and wave aberration.

The bidimensional phase-transfer function (PTF) of the human eye has been computed from aerial retinal images of a point test. These images were previously determined by using a recently developed hybrid optical-digital method. Actual PTF data have been obtained directly without linear variations with spatial frequency and have shown great variations among individual subjects. The influence of the PTF on the determination of the point-spread function and the wave-aberration function for emmetropized and slightly astigmatic subjects has been also evaluated. Finally, the effect of pupil size on the PTF was determined by computing these functions from the wave aberration. These results allow us to give a more thorough description of the optical image quality of the human eye and can be used as actual data in subsequent psychophysical studies.The authors thank M. Nieto-Vesperinas for his critical reading of the manuscript. This research was supported by the Comision Asesora de Investigaci6n Cientifica y T6cnica (grant 2520/83), Ministerio de Educaci6n y Ciencia, Spain.Peer Reviewe