Algebraic Curves

We build now a nearly free vector bundle with exponents (a+1, b +1) by adding one line (the blue line in Figure 5) passing through a − 1 triple points to the free arrangement C 0

Given a pencil of algebraic plane curves such that a general element is irreducible, the purpose of this paper is to give a sharp upper bound for the number of reducible curves in

coordinate functions satisfy will give some equations that define the curve and that allow us to compute its points..

We illustrate the general theory with a discussion of real hyper-elliptic curves in paragraph 6, real plane curves in paragraph 7, and real trigonal curves in paragraph 8, and end

In fact, up to permutation of the entries, there are 1054 numerical types of exceptional curves E on the blow up X of P 2 at r = 9 generic points such that the image of E is a curve

It is plausible, however, that one might bound the number of algebraic families occurring in Corollary 4.4, and therefore get an effective bound on the number

A complex algebraic curve is isomorphic to a curve defined by real polynomials if and only if the correspond- ing Riemann surface admits an antiholomorphic

Oda: Vector bundles on the elliptic curve, Nagoya Math. Pardini: Some remarks on plane curves over fields of finite characteristic,