منابع مشابه
Algebraic Curves
We consider the problem of tracing algebraic curves by computer, using a numerical technique augmented by symbolic computations. In particular, all singularities are analyzed cOITectly. The methods presented find application in solid modeling and robotics.
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If algebraic varieties like curves or surfaces are to be manipulated by computers, it is essential to be able to represent these geometric objects in an appropriate way. For some applications an implicit representation by algebraic equations is desirable, whereas for others an explicit or parametric representation is more suitable. Therefore, transformation algorithms from one representation to...
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1.1. Sheaves. Let X be a topological space. A sheaf F on X associates to each open set U an abelian group F (U), called the sections of F over U , along with a restriction map rV,U : F (V ) → F (U) for any open sets U ⊂ V (for a section σ ∈ F (V ), we often write σ|U to denote rV,U (σ)), satisfying the following conditions: (1) For any open sets U ⊂ V ⊂W , rV,U ◦ rW,V = rW,U ; (2) For a collect...
متن کاملAlgebraic Curves/Fall 2015
(Algebra) It’s a complex projective manifold C of dimension one. As such, it has a field of rational functions K(C) of transcendence degree one over the field C of scalars. The curve can be recovered from the field as the set of discrete valuation rings of K/C, which has the “natural” structure of a projective manifold. There is a canonical line bundle ωC , whose degree captures the genus via d...
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ژورنال
عنوان ژورنال: Topology
سال: 2002
ISSN: 0040-9383
DOI: 10.1016/s0040-9383(00)00023-9