TL;DR
This paper introduces a method for computing projective isomorphisms between rational surfaces by reducing the problem to five base cases through parametric map modifications, applicable to various types of surface isomorphisms.
Contribution
The paper presents a novel approach to compute projective isomorphisms between rational surfaces by simplifying the problem to five base cases using degree-lowering modifications.
Findings
Efficient computation of projective isomorphisms between rational surfaces.
Applicable to affine, Euclidean, and Möbius surface isomorphisms.
Reduces complex problems to manageable base cases.
Abstract
We present a method for computing projective isomorphisms between rational surfaces that are given in terms of their parametrizations. The main idea is to reduce the computation of such projective isomorphisms to five base cases by modifying the parametric maps such that the components of the resulting maps have lower degree. Our method can be used to compute affine, Euclidean and M\"obius isomorphisms between surfaces.
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