Projective isomorphisms between rational surfaces. (English) Zbl 1483.14077
This article is concerned with the computation of all projective (and also affine, Euclidean or Möbius) isomorphisms between to rational parametric surfaces. The surfaces are assumed to be of dimension two but the dimension of the ambient projective space is not restricted.
Projective isomorphisms are indirectly computed via “compatible” birational maps of their respective parameter domains, taking into account the blow-up of base points and the contraction of lines. The fundamental strategy, which is cast into an algorithm and partially implemented in SageMath, reduces the problem to the case of surfaces that are covered by straight lines or conics. More specifically, only five base cases need to be considered. Two of them discussed in this article, the three remaining cases are left as future work.
Projective isomorphisms are indirectly computed via “compatible” birational maps of their respective parameter domains, taking into account the blow-up of base points and the contraction of lines. The fundamental strategy, which is cast into an algorithm and partially implemented in SageMath, reduces the problem to the case of surfaces that are covered by straight lines or conics. More specifically, only five base cases need to be considered. Two of them discussed in this article, the three remaining cases are left as future work.
Reviewer: Hans-Peter Schröcker (Innsbruck)
MSC:
| 14J50 | Automorphisms of surfaces and higher-dimensional varieties |
| 14J26 | Rational and ruled surfaces |
| 14Q10 | Computational aspects of algebraic surfaces |
Keywords:
projective isomorphisms; surface automorphisms; rational surfaces; del Pezzo surfaces; adjunctionSoftware:
SageMathReferences:
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