Rational Parametrizations of Algebraic Curves using a Canonical Divisor

Rational Parametrizations of Algebraic Curves Using a Canonical Divisor

For an algebraic curve C with genus 0 the vector space L(D) where D is a divisor of degree 2 gives rise to a bijective morphism g from C to a conic C 2 in the projective plane. We present an algorithm that uses an integral basis for computing L(D) for a suitably chosen D. The advantage of an integral basis is that it contains all the necessary information about the singularities, so once the in...

Rational Algebraic Curves: A Computer Algebra Approach

Algebraic geometry is a central field within mathematics which is often viewed as difficult for outsiders to enter. Recent years have seen many books which present various topics of algebraic geometry from a computational viewpoint, thereby making the subject more accessible. The book under review, RAC for short, is part of this positive trend. Its main focus is parametrizing rational plane alg...

The Degree of the Divisor of Jumping Rational Curves

For a semistable reflexive sheaf E of rank r and c1 = a on P n and an integer d such that r|ad, we give sufficient conditions so that the restriction of E on a generic rational curve of degree d is balanced, i.e. a twist of the trivial bundle (for instance, if E has balanced restriction on a generic line, or r = 2 or E is an exterior power of the tangent bundle). Assuming this, we give a formul...

Acquisition of Rational Points on Algebraic Curves

Geometry of Rational Curves on Algebraic Varieties

Geometry of Rational Curves on Algebraic Varieties