Ruled surfaces have been studied by NAGATA IS], MARUYAMA [3, 41 and other authors from the point of view of classification. Especially on rational ruled surfaces we have known many facts, for example, an explicit condition for a divisor D to be ample, that for ID( to have an irreducible member and s
Birational Morphisms of Rational Surfaces
β Scribed by Brian Harbourne
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 253 KB
- Volume
- 190
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
β¦ Synopsis
A fairly complete characterization on anticanonical rational surfaces of the divisor classes whose sections define birational morphisms is given. Most results are proven over an algebraically closed field of arbitrary characteristic.
π SIMILAR VOLUMES
## Abstract Let __L__ be a nef line bundle on a Del Pezzo surface. We show that __L__ + __K~S~__ is birationally __k__βvery ample if and only if all the smooth curves in |__L__| have gonality β₯__k__ + 2, and we also find numerical criteria for birational __k__βvery ampleness.
The parametrization problem asks for a parametrization of an implicitly given surface, in terms of rational functions in two variables. We give an algorithm that decides if such a parametric representation exists, based on Castelnuovo's rationality criterion. If the answer is yes, then we compute su
A generalized projective implicitization theorem is presented that can be used to solve the implicitization of rational parametric curves and surfaces in an affine space. The Groebner bases technique is used to implement the algorithm. The algorithm has the advantages that it can handle base points
A canal surface is the envelope of a one-parameter set of spheres with radii r(t) and centers m(t). It is shown that any canal surface to a rational spine curve m(t) and a rational radius function r(t) possesses rational parametrizations. We derive algorithms for the computation of these parametriza