منابع مشابه
Curves of constant diameter and inscribed polygons
If one drops the unicity assumption, (C(D)) is the property of having constant diameter, which is in fact equivalent (for closed curves in the plane) to having constant width or constant breadth (for the definitions and the proof of the equivalence, see [8, chap. 25]). It is a surprise to many (including me !) that curves of constant diameter other that the circle do exist. The simplest example...
متن کاملBezout Curves in the Plane
First, recall how Bezout’s Theorem can be made more precise by specifying the meaning of the word “generically” used above, using elementary scheme-theoretic language ([H, II]). Fix an algebraically closed field k. There is little loss in assuming k = C (until Section 3). Since we work over an algebraically closed field, we often identify reduced algebraic sets with their k-valued points. In th...
متن کاملCurves in the Double Plane
We study in detail locally Cohen-Macaulay curves in P 3 which are contained in a double plane 2H , thus completing the classification of curves lying on surfaces of degree two. We describe the irreducible components of the Hilbert schemes Hd,g(2H) of locally Cohen-Macaulay curves in 2H of degree d and arithmetic genus g, and we show that Hd,g(2H) is connected. We also discuss the Rao module of ...
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, ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1961
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1961-0120604-3