双分次双有理映射的有效判据
Effective criteria for bigraded birational maps
摘要：
本文考虑有理映射的源是两个子簇的乘积，每一个子簇嵌入在射影空间中。我们的主要目标是调查这样的地图的双理性准则。首先，给出了一个一般的标准，在秩的一对矩阵，成为已知的雅可比对偶矩阵。然后，我们专注于有理映射从产品的两个projectine线的射影平面在非常低的bidegrees和提供新的矩阵为基础的双合理性准则，通过分析syzygies的定义方程的地图，特别是通过查看的syzygy模块的某些bigrated部分的尺寸。最后，我们的结果的几何造型的背景下，讨论了在本文的最后。
英文摘要：
In this paper, we consider rational maps whose source is a product of two subvarieties, each one being embedded in a projective space. Our main objective is to investigate birationality criteria for such maps. First, a general criterion is given in terms of the rank of a couple of matrices that became to be known as Jacobian dual matrices. Then, we focus on rational maps from the product of two projectine lines to the projective plane in very low bidegrees and provide new matrix-based birationality criteria by analyzing the syzygies of the defining equations of the map, in particular by looking at the dimension of certain bigraded parts of the syzygy module. Finally, applications of our results to the context of geometric modeling are discussed at the end of the paper.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
