Algebraic curve - Wikipedia
In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables.
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theory of algebraic curves from the viewpoint of modern algebraic geometry, but without excessive prerequisites. We have assumed that the reader is familiar with some basic properties of rings, ideals, and polynomials, such as is often covered in a one-semester course in mod-ern algebra; additional commutative algebra is developed in later ...
Eight Basic Algebraic Curves - dummies
Mar 26, 2016 · Algebra is all about graphing relationships, and the curve is one of the most basic shapes used. Here's a look at eight of the most frequently used graphs.
An algebraic curve is the subset of the plane formed by the solutions (x, y) of a non-constant polynomial equation in two variables, (19.1) C = {(x, y) ∈ R2 : f(x, y) = 0}. To make our language more precise, let’s say that xiyj is a monomial of degree i + j. Then, a polynomial of degree ≤ d is a sum of monomials.
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Curves can appear in the abstract and in projective space. An important part of understanding curves is how they vary in flat families. The differ-ence between ACGH volumes 1 and 2, is that 1 deals with a fixed curve and 2 deals with families of curves. To learn more on families of curves, look at Moduli of Curves.
Algebraic curve - Encyclopedia of Mathematics
Dec 17, 2019 · An algebraic curve is the most frequently studied object in algebraic geometry. In the sequel, an algebraic curve means an irreducible algebraic curve over an algebraically closed field. The simplest and clearest concept is that of a plane affine algebraic curve.
algebraic curves as a smooth projective curve (given by explicit equations), and an explicit divisor, there is an algorithm to determine the space L(D). We’ll do that in a week or two. The one thing to observe is that there’s a certain redundancy here, in this problem.
Algebraic Curve -- from Wolfram MathWorld
Oct 10, 2024 · Algebraic Curve. An algebraic curve over a field is an equation , where is a polynomial in and with coefficients in . A nonsingular algebraic curve is an algebraic curve over which has no singular points over . A point on an algebraic curve is simply a solution of the equation of the curve.