Generic coverings of plane with A-D-E-singularities

We generalize results of the paper math.AG/9803144, in which Chisini's conjecture on the unique reconstruction of f by the curve B is investigated. For this fibre products of generic coverings are studied. The main inequality bounding the degree of a covering in the case of existence of two nonequivalent coverings with the branch curve B is obtained. This inequality is used for the proof of the Chisini conjecture for m-canonical coverings of surfaces of general type for $m\ge 5$.Comment: 43 pages, 20 figures; to appear in Izvestiya Mat

On braid monodromy factorizations

We introduce and develop a language of semigroups over the braid groups for a study of braid monodromy factorizations (bmf's) of plane algebraic curves and other related objects. As an application we give a new proof of Orevkov's theorem on realization of a bmf over a disc by algebraic curves and show that the complexity of such a realization can not be bounded in terms of the types of the factors of the bmf. Besides, we prove that the type of a bmf is distinguishing Hurwitz curves with singularities of inseparable types up to $H$-isotopy and $J$-holomorphic cuspidal curves in \C P^2 up to symplectic isotopy.Comment: 52 pages, AMS-Te

Regular homotopy of Hurwitz curves

We prove that any two irreducible cuspidal Hurwitz curves $C_0$ and $C_1$ (or more generally, curves with A-type singularities) in the Hirzebruch surface $F_N$ with coinciding homology classes and sets of singularities are regular homotopic; and symplectically regular homotopic if $C_0$ and $C_1$ are symplectic with respect to a compatible symplectic form.Comment: 26 page

Models and phenomenology

It is evident that models of the knee should match the observational phenomenology. In this talk I discuss a few aspects of phenomenology, which are important not only for the understanding of the knee origin, but also for the general problem of the origin of cosmic rays. Among them are the shape of the energy spectrum, its irregularity, the sharpness of the knee and its fine structure. The classification of models is given and some examples of the most recent models are discussed. The most probable conclusion deduced from this examination is that the knee has an astrophysical origin and the so called 'source' models of the knee are most likely among them.Comment: 13 pages, 4 figures, overview talk at 19th European Cosmic Ray Symposium, Firenze, Italy, 30.08-4.09.2004 (to be published in the Int.J.Mod.Phys.A

On the upper limit of antinuclei content in cosmic rays

Upper limit of antinuclei content in cosmic ray