649 research outputs found

    Geography of irreducible plane sextics

    No full text
    We complete the equisingular deformation classification of irreducible singular plane sextic curves. As a by-product, we also compute the fundamental groups of the complement of all but a few maximizing sextics

    Lines on quartic surfaces

    No full text

    On the Artal-Carmona-Cogolludo construction

    Get PDF
    Cataloged from PDF version of article.We derive explicit defining equations for a number of irreducible maximizing plane sextics with double singular points only. For most real curves, we also compute the fundamental group of the complement; all groups found are abelian, which suffices to complete the computation of the groups of all non-maximizing irreducible sextics. As a by-product, examples of Zariski pairs in the strongest possible sense are constructed. © 2014 World Scientific Publishing Company

    The Alexander module of a trigonal curve

    Get PDF
    Cataloged from PDF version of article.We describe the Alexander modules and Alexander polynomials (both over ℚ and over finite fields Fp) of generalized trigonal curves. The rational case is completely resolved; in the case of characteristic p > 0, a few points remain open. The results obtained apply as well to plane curves with deep singularities. © European Mathematical Society.We describe the Alexander modules and Alexander polynomials (both over Q and over finite fields Fp) of generalized trigonal curves. The rational case is closed completely; in the case of characteristic p > 0, a few points remain open. The results obtained apply as well to plane curves with deep singularities

    Transcendental lattice of an extremal elliptic surface

    Get PDF
    Cataloged from PDF version of article.We develop an algorithm computing the transcendental lattice and the Mordell-Weil group of an extremal elliptic surface. As an example, we compute the lattices of four exponentially large series of surfaces

    Stable symmetries of plane sextics

    Get PDF
    We classify projective symmetries of irreducible plane sextics with simple singularities which are stable under equivariant deformations. We also outline a connection between order~2 stable symmetries and maximal trigonal curves

    Conics in sextic K3K3-surfaces in P4\mathbb{P}^4

    Get PDF
    We prove that the maximal number of conics in a smooth sextic K3K3-surface XP4X\subset\mathbb{P}^4 is 285, whereas the maximal number of real conics in a real sextic is 261. In both extremal configurations, all conics are irreducible
    corecore