Contributions to projective theory of singular points of space curves
نویسندگان
چکیده
منابع مشابه
5 Local Parametrization of Space Curves at Singular Points
We propose a symbolic computation algorithm for computing local parametrization of analytic branches and real analytic branches of a curve in n-dimensional space, which is de ned by implicit polynomial equations. The algorithm can be used in space curve tracing near a singular point, as an alternative to symbolic computations based on resolutions of singularities.
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ly isomorphic to (C×)r−1 × (C), and hence also to (S1)r−1 × (R), where r = |J | is the number of branches and k = δ(C)− r+1 = 1 2 (μ(C) + 1 − r). The construction of the Jacobian variety J(C̃) of the non-singular curve C̃ in the large is standard in algebraic geometry. There is also a notion of Jacobian of a singular curve C , defined e.g. in [85], which, like the other, is an abelian group. Ther...
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We compute the singular points of a plane rational curve, parametrically given, using the implicitization matrix derived from the μ-basis of the curve. It is shown that singularity factors, which are defined and uniquely determined by the elementary divisors of the implicitization matrix, contain all the information about the singular points, such as the parameter values of the singular points ...
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We examine the problem of finding rational points defined over solvable extensions on algebraic curves defined over general fields. We construct non-singular, geometrically irreducible projective curves without solvable points of genus g when g is at least 40 over fields of arbitrary characteristic. We prove that every smooth, geometrically irreducible projective curve of genus 0, 2, 3 or 4 def...
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We survey and expand 1 on the work of Segal, Milgram and the author on the topology of spaces of maps of positive genus curves into complex projective space (in both the holomorphic and continuous categories). Both based and unbased maps are studied and in particular we compute the fundamental groups of the spaces in question. The relevant case when n = 1 is given by a non-trivial extension whi...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1947
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1947-0020829-4