论文标题
在表面参数化的基点基因座上：公式和后果
On the base point locus of surface parametrizations: formulas and consequences
论文作者
论文摘要
本文表明，投影有理表面参数化的基数基因座的多样性可以表示为单变量结果的含量。结果，我们获得了与表面程度，参数化程度，基本点多样性的程度以及由参数化引起的理性图的程度有关的新的证明。此外，我们将这两个公式扩展到了射影平面的主要有理图的情况下，并描述了参数化的基础基因座及其重新构度的基础基因座如何相关。作为这些结果的应用，我们探讨了表面重新训练的程度如何受基点的存在影响。
This paper shows that the multiplicity of the base points locus of a projective rational surface parametrization can be expressed as the degree of the content of a univariate resultant. As a consequence, we get a new proof of the degree formula relating the degree of the surface, the degree of the parametrization, the base points multiplicity, and the degree of the rational map induced by the parametrization. In addition, we extend both formulas to the case of dominant rational maps of the projective plane and describe how the base point loci of a parametrization and its reparametrizations are related. As an application of these results, we explore how the degree of a surface reparametrization is affected by the presence of base points.
