库马尔通信的实施
Implementation of Kumar's correspondence
摘要：
1997年，N.M.库马尔发表了一份文件，介绍了一种新的工具，使用建设代数向量丛。给定射影n-空间上的一个向量丛，Quillen-Suslin的一个著名定理保证了在射影n-空间中超平面的补上生成该丛的截面的存在性。Kumar利用这一事实给出了满足一定条件的射影n-空间上的向量丛与射影（n-1）-空间上的向量丛之间的对应关系。然后，他应用这种对应关系，以建立存在许多，以前未知的，秩二束投射fourspace积极的特点。本论文的目标是给出一个明确的同调描述库马尔的对应关系，在适当的计算机代数系统中实现的设置。
英文摘要：
In 1997, N.M. Kumar published a paper which introduced a new tool of use in the construction of algebraic vector bundles. Given a vector bundle on projective n-space, a well known theorem of Quillen-Suslin guarantees the existence of sections which generate the bundle on the complement of a hyperplane in projective n-space. Kumar used this fact to give a correspondence between vector bundles on projective n-space and vector bundles on projective (n-1)-space satisfying certain conditions. He then applied this correspondence to establish the existence of many, previously unknown, rank two bundles on projective fourspace in positive characteristic. The goal of the present paper is to give an explicit homological description of Kumar's correspondence in a setting appropriate for implementation in a computer algebra system.
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。
