منابع مشابه
Polynomial of Sextics
Alexander polynomials of sextics are computed in the case of sextics with only simple singularities or sextics of torus type with arbitrary singularities. We will show that for irreducible sextics, there are only 4 possible Alexander polynomials: (t 2 −t+1) j , j = 0, 1, 2, 3. For the computation, we use the method of Esnault-Artal and the classification result in our previous papers.
متن کاملFundamental Groups of Symmetric Sextics
We study the moduli spaces and compute the fundamental groups of plane sextics of torus type with at least two type E6 singular points. As a simple application, we compute the fundamental groups of 125 other sextics, most of 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 کاملZariski Pairs on Sextics Ii
We continue to study Zariski pairs in sextics. In this paper, we study Zariski pairs of sextics which are not irreducible. The idea of the construction of Zariski partner sextic for reducible cases is quit different from the irreducible case. It is crucial to take the geometry of the components and their mutual intersection data into account. When there is a line component, flex geometry (i.e.,...
متن کاملElliptic Curves from Sextics
Let N be the moduli space of sextics with 3 (3,4)-cusps. The quotient moduli space N/G is one-dimensional and consists of two components, Ntorus/G and Ngen/G. By quadratic transformations, they are transformed into one-parameter families Cs and Ds of cubic curves respectively. First we study the geometry of Nε/G, ε = torus, gen and their structure of elliptic fibration. Then we study the Mordel...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2014
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2014.05.023