منابع مشابه
Monodromy Groups of Hurwitz-type Problems
We solve the Hurwitz monodromy problem for degree 4 covers. That is, the Hurwitz space H4,g of all simply branched covers of P of degree 4 and genus g is an unramified cover of the space P2g+6 of (2g + 6)-tuples of distinct points in P. We determine the monodromy of π1(P2g+6) on the points of the fiber. This turns out to be the same problem as the action of π1(P2g+6) on a certain local system o...
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The article contains several problems concerning local monodromy groups of singularities, Lyashko–Looijenga maps, integral geometry, and topology of spaces of real algebraic manifolds.
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Let m ≥ 2 and r ≥ 1 be integers and let c ∈ Zm = {0, 1, . . . , m− 1}. In this paper, we give an upper bound and a lower bound for the number of unordered solutions x1, . . . , xn ∈ Zm of the congruence x1 + x2 + · · · + xr ≡ c mod m. Exact formulae are also given when m or r is prime. This solution number involves the Catalan number or generalized Catalan number in some special cases. Moreover...
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For the polynomial planar vector fields with a hyperbolic or nilpotent critical point at the origin, the monodromy problem has been solved, but for the strongly degenerate critical points this problem is still open. When the critical point is monodromic, the stability problem or the center- focus problem is an open problem too. In this paper we will consider the polynomial planar vector fields ...
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It is by now well known that the parities of the binomial coefficients show a fractal-like appearance when plotted in the x-y plane. Similarly, if f(n,k) is some counting sequence and/? is a prime, we can plot an asterisk at (//,&) iff(n,k) # 0 (mod/?), and a blank otherwise, to get other complex, and often interesting, patterns. For the ordinary and Gaussian binomial coefficients and for the S...
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1968
ISSN: 0025-5645
DOI: 10.2969/jmsj/02010107