Discrminantal Groups and Zariski Pairs of Sextic Curves
نویسندگان
چکیده
A series of Zariski pairs and four Zariski triplets were found by using lattice theory of K3 surfaces. There is a Zariski triplet of which one member is a deformation of another.
منابع مشابه
On Deformations of Singular Plane Sextics
We study complex plane projective sextic curves with simple singularities up to equisingular deformations. It is shown that two such curves are deformation equivalent if and only if the corresponding pairs are diffeomorphic. A way to enumerate all deformation classes is outlined, and a few examples are considered, including classical Zariski pairs; in particular, promising candidates for homeom...
متن کاملLATTICE ZARISKI k-PLES OF PLANE SEXTIC CURVES AND Z-SPLITTING CURVES FOR DOUBLE PLANE SEXTICS
A simple sextic is a reduced complex projective plane curve of degree 6 with only simple singularities. We introduce a notion of Z-splitting curves for the double covering of the projective plane branching along a simple sextic, and investigate lattice Zariski k-ples of simple sextics by means of this notion. Lattice types of Z-splitting curves and their specializations are defined. All lattice...
متن کاملA weighted version of Zariski’s hyperplane section theorem and fundamental groups of complements of plane curves
In this paper, we formulate and prove a weighted homogeneous version of Zariski’s hyperplane section theorem on the fundamental groups of the complements of hypersurfaces in a complex projective space, and apply it to the study of π1(P 2 \C), where C ⊂ P is a projective plane curve. The main application is to prove a comparison theorem as follows. Let φ : P → P be the composition of the Verones...
متن کاملA Zariski Pair in Affine Complex Plane
We present a Zariski pair in affine complex plane consisting of two line arrangements, each of which has six lines. In the seminal paper [3], Zariski started the study of the fundamental groups of the complements of plane algebraic curves. Among other things, he constructed a pair of plane curves with the same degree and the same local singularities, but non-isomorphic fundamental groups, which...
متن کاملOka’s Conjecture on Irreducible Plane Sextics
We partially prove and partially disprove Oka’s conjecture on the fundamental group/Alexander polynomial of an irreducible plane sextic. Among other results, we enumerate all irreducible sextics with simple singularities admitting dihedral coverings and find examples of Alexander equivalent Zariski pairs of irreducible
متن کامل