A Representation Theorem for Generic Line Arrangements in the Plane
نویسندگان
چکیده
منابع مشابه
Topology of Generic Line Arrangements
Our aim is to generalize the result that two generic complex line arrangements are equivalent. In fact for a line arrangement A we associate its defining polynomial f = ∏ i(aix + biy + ci), so that A = (f = 0). We prove that the defining polynomials of two generic line arrangements are, up to a small deformation, topologically equivalent. In higher dimension the related result is that within a ...
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Let ∆A(n, d) denote the largest possible average diameter of a bounded cell of a simple arrangement defined by n hyperplanes in dimension d. We have ∆A(n, 2) ≤ 2+ 2 n−1 in the plane, and ∆A(n, 3) ≤ 3+ 4 n−1 in dimension 3. In general, the average diameter of a bounded cell of a simple arrangement is conjectured to be less than the dimension; that is, ∆A(n, d) ≤ d. We propose line and plane arra...
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ژورنال
عنوان ژورنال: The Journal of the Indian Mathematical Society
سال: 2020
ISSN: 2455-6475,0019-5839
DOI: 10.18311/jims/2020/24873