منابع مشابه
The Limiting Curve of Jarník’s Polygons
VQ = {(q, a) ∈ Z : gcd(q, a) = 1, max{|a|, |q|} ≤ Q}. Then the Jarńık polygon PQ is the unique (up to translation) convex polygon whose sides are precisely the vectors in VQ. In other words, PQ is the polygon whose vertices can be obtained by starting from an arbitrary point in R and adding the vectors in VQ one by one, traversing those vectors in a counterclockwise direction. For example, the ...
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We give a combinatorial upper bound for the gonality of a curve that is defined by a bivariate Laurent polynomial with given Newton polygon. We conjecture that this bound is generically attained, and provide proofs in a considerable number of special cases. One proof technique uses recent work of M. Baker on linear systems on graphs, by means of which we reduce our conjecture to a purely combin...
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We have made a conceptual error in the construction of our regular strongly semistable arithmetic surface X over C[[t]], as explained in [2, Sect. 7]. The error lies in the last part, involving toric resolutions of singularities. Namely, it has been overlooked that the exceptional curves that are introduced during the resolution may appear with non-trivial multiplicities, turning X non-stable. ...
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Stimulated by recent work by Gregory and Qu, it is shown that the limit of local corner cutting is a continuously differentiable curve in case the corners of the iterates become increasingly flat.
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with α 6= 0, and initial condition x(p, 0) = x0(p). This produces a family of curves γt = x(S, t). Here κ is the curvature, and n is the outward-pointing unit normal vector. These equations are particularly natural in that they are isotropic (equivariant under rotations in the plane) and homogeneous (equivariant under dilation of space, if time is also scaled accordingly). The main aim of this ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2003
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-03-03219-7