Polar Cremona transformations.
نویسندگان
چکیده
منابع مشابه
Polar Cremona Transformations and Monodromy of Polynomials
Consider the gradient map associated to any non-constant homogeneous polynomial f ∈ C[x0, . . . , xn] of degree d, defined by φf = grad(f) : D(f) → P , (x0 : . . . : xn) → (f0(x) : . . . : fn(x)) whereD(f) = {x ∈ P; f(x) 6= 0} is the principal open set associated to f and fi = ∂f ∂xi . This map corresponds to polar Cremona transformations. In Proposition 3.4 we give a new lower bound for the de...
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Consider the gradient map associated to any non-constant homogeneous polynomial f ∈ C[x0, . . . , xn] of degree d, defined by φf = grad(f) : D(f) → P, (x0 : . . . : xn) 7→ (f0(x) : . . . : fn(x)) where D(f) = {x ∈ P; f(x) 6= 0} is the principal open set associated to f and fi = ∂f ∂xi . This map corresponds to the polar Cremona transformations considered by Dolgachev in [10], see also [9], [8],...
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In 1883 Kantor' stated and attempted a demonstration of a theorem which asserted that the satisfaction of a system of equations by a certain set of positive integers was sufficient to assure that these integers would represent a planar Cremona transformation. Since then the theorem has been repeated several times in the literature. Recently Coolidge2 attached new significance to the theorem and...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 2000
ISSN: 0026-2285
DOI: 10.1307/mmj/1030132714