Kähler structure on Hurwitz spaces
نویسندگان
چکیده
منابع مشابه
Counting Ramified Coverings and Intersection Theory on Hurwitz Spaces Ii (local Structure of Hurwitz Spaces and Combinatorial Results)
The Hurwitz space is a compactification of the space of rational functions of a given degree. We study the intersection of various strata of this space with its boundary. A study of the cohomology ring of the Hurwitz space then allows us to obtain recurrence relations for certain numbers of ramified coverings of a sphere by a sphere with prescribed ramifications. Generating functions for these ...
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1.1 The classical Hurwitz space and the moduli of curves The classical Hurwitz space first appeared in the work of Clebsch [5] and Hurwitz [17] as an auxiliary object to study the moduli space of curves. Let X be a smooth projective curve of genus g over C. A rational function f : X → P of degree n is called simple if there are at least n − 1 points on X over every point of P. Such a cover has ...
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Deformations of Dubrovin’s Hurwitz Frobenius manifolds are constructed. The deformations depend on g(g+1)/2 complex parameters where g is the genus of the corresponding Riemann surface. In genus one, the flat metric of the deformed Frobenius manifold coincides with a metric associated with a one-parameter family of solutions to the Painlevé-VI equation with coefficients (1/8,−1/8, 1/8, 3/8) . A...
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The Hurwitz space approach to the regular Inverse Galois Problem was the only successful approach to Galois group realizations beyond nilpotent groups. It gave regular realizations of many series of groups. More significantly, the M(odular) T(ower) program identified obstructions to systematically finding regular realizations. Finding a way around those obstructions generalize renown results on...
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Here we solve N × N Riemann-Hilbert (inverse monodromy) problems with all monodromy matrices having the structure of matrices of quasi-permutation (i.e. matrices which have only one non-zero element in each column and each row). Such RiemannHilbert problem may be associated to arbitrary Hurwitz space of algebraic curves L of genus g realized as N -sheeted covering over CP1, and allowes solution...
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ژورنال
عنوان ژورنال: Manuscripta Mathematica
سال: 2015
ISSN: 0025-2611,1432-1785
DOI: 10.1007/s00229-015-0738-6