منابع مشابه
On Complete Arcs Arising from Plane Curves
We point out an interplay between Fq-Frobenius non-classical plane curves and complete (k, d)-arcs in P2(Fq). A typical example that shows how this works is the one concerning an Hermitian curve. We present some other examples here which give rise to the existence of new complete (k, d)-arcs with parameters k = d(q − d + 2) and d = (q − 1)/(q − 1), q being a power of the characteristic. In addi...
متن کاملShortening Curves on Surfaces
METHODS of shortening a curve in a manifold have been used to establish the existence of closed geodesics, and in particular of simple closed geodesics on 2-spheres. For this purpose, a curve evolution process should (a) not increase the number of self-intersections of a curve, (b) exist for all time or until a curve collapses to a point, (c) shorten curves sufficiently fast so that curves whic...
متن کاملReal Plane Algebraic Curves
We study real algebraic plane curves, at an elementary level, using as little algebra as possible. Both cases, affine and projective, are addressed. A real curve is infinite, finite or empty according to the fact that a minimal polynomial for the curve is indefinite, semi–definite nondefinite or definite. We present a discussion about isolated points. By means of the operator, these points can ...
متن کاملOn submaximal plane curves
We prove that a submaximal curve in P has sequence of multiplicities (μ, ν, . . . , ν), with μ < sν for every integer s with (s− 1)(s+ 2) ≥ 6.76( r − 1). This note is a sequel to [10], where a specialization method was developed in order to bound the degree of singular plane curves. The problem under consideration is, given a system of multiplicities (m) = (m1,m2, . . . ,mr) ∈ Z and points p1, ...
متن کاملDuality of Plane Curves
The dual of an algebraic curve C in RP defined by the polynomial equation f(x, y, z) = 0 is the locus of points ( ∂f ∂x (a, b, c) : ∂f ∂y (a, b, c) : ∂f ∂z (a, b, c) ) where (a : b : c) ∈ C. The dual can alternatively be defined geometrically as the image under reciprocation of the envelope of tangent lines to the curve. It is known that the dual of an algebraic curve is also an algebraic curve...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1998
ISSN: 0022-040X
DOI: 10.4310/jdg/1214424967