649 research outputs found
Geography of irreducible plane sextics
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
On the Artal-Carmona-Cogolludo construction
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
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
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
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 -surfaces in
We prove that the maximal number of conics in a smooth sextic -surface is 285, whereas the maximal number of real conics in a real sextic is 261. In both extremal configurations, all conics are irreducible
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