多阶有理映射的纤维及其在有理曲面上的正交投影

IF 1.6 2区 数学 Q2 MATHEMATICS, APPLIED
Nicolás Botbol, Laurent Bus'e, M. Chardin, Fatmanur Yildirim
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引用次数: 2

摘要

我们提出了一种新的计算点在三维投影空间中嵌入的有理代数曲面上的正交投影的代数方法。这个问题首先转化为一般有限占优有理映射的有限纤维的计算:法线到有理曲面的同余。然后,深入研究了与这种同余相关的某些协同模块,并在一些一般性假设下应用于构建提供其有限纤维的通用表示的消除矩阵。这些矩阵线性地依赖于三维空间的变量。它们可以预先计算,以便用快速和鲁棒的数值线性代数计算近似计算点的正交投影。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Fibers of Multi-Graded Rational Maps and Orthogonal Projection onto Rational Surfaces
We contribute a new algebraic method for computing the orthogonal projections of a point onto a rational algebraic surface embedded in the three dimensional projective space. This problem is first turned into the computation of the finite fibers of a generically finite dominant rational map: a congruence of normal lines to the rational surface. Then, an in-depth study of certain syzygy modules associated to such a congruence is presented and applied to build elimination matrices that provide universal representations of its finite fibers, under some genericity assumptions. These matrices depend linearly in the variables of the three dimensional space. They can be pre-computed so that the orthogonal projections of points are approximately computed by means of fast and robust numerical linear algebra calculations.
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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
19
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