In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous …

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 …

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 …

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 …

curves. 0BXY Lemma 2.1. Let kbe a field. LetX be a curve and Y a proper variety. Let U ⊂X be a nonempty open and let f: U →Y be a morphism. If x∈X is a closed point such that O X,x is a …

5 days ago · An algebraic curve over a field K is an equation f(X,Y)=0, where f(X,Y) is a polynomial in X and Y with coefficients in K. A nonsingular algebraic curve is an algebraic …

We show one can construct algebraic curves passing through a given finite collection of points in the plane (interpolation). We look at other ways in which algebraic curves can arise, through …

An algebraic curve is a curve which is described by a polynomial equation: f(x,y) = X aijx iyj= 0 in xand y. The degree of the curve is the degree of the polynomial f(x,y). A parametric curve α(t) …

An algebraic curve is an algebraic variety each of whose irreducible components has dimension one; a plane algebraic curve is an algebraic curve of codimension one, i.e.

We see some of the purely algebraic results reappearing topologically. The last section contains some exercises about rational curves. 1. Families of Plane Curves. Formula 1.1. The …