Hilbert Problem 15 and Ritt-Wu Method(Ⅰ)

详细信息    查看全文 | 推荐本文 |

英文篇名：Hilbert Problem 15 and Ritt-Wu Method(Ⅰ) 作者：LI ; Banghe 英文作者：LI Banghe;KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences; 英文关键词：Cubed curves with cusp;;Hilbert Problem 15;;Ritt-Wu Method 中文刊名：XTYW 英文刊名：系统科学与复杂性学报(英文版) 机构：KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences; 出版日期：2019-02-15 出版单位：Journal of Systems Science & Complexity 年：2019 期：v.32 语种：英文; 页：XTYW201901004 页数：15 CN：01 ISSN：11-4543/O1 分类号：51-65

摘要

Hilbert problem 15 requires to understand Schubert's book. In this book, there is a theorem in §23, about the relation of the tangent lines from a point and the singular points of cubed curves with cusp near a 3-multiple straight line, which was obtained by the so called main trunk numbers, while for these numbers, Schubert said that he obtained them by experiences. So essentially Schubert even did not give any hint for the proof of this theorem. In this paper, by using the concept of generic point in the framework of Van der Waerden and Weil on algebraic geometry, and realizing Ritt-Wu method on computer, the authors prove that this theorem of Schubert is completely right.
        Hilbert problem 15 requires to understand Schubert's book. In this book, there is a theorem in §23, about the relation of the tangent lines from a point and the singular points of cubed curves with cusp near a 3-multiple straight line, which was obtained by the so called main trunk numbers, while for these numbers, Schubert said that he obtained them by experiences. So essentially Schubert even did not give any hint for the proof of this theorem. In this paper, by using the concept of generic point in the framework of Van der Waerden and Weil on algebraic geometry, and realizing Ritt-Wu method on computer, the authors prove that this theorem of Schubert is completely right.

引文

[1]Schubert H,Kalkül der abz?hlenden Geometrie,Springer-Verlag,1979.
    [2]Van der Waerden,Einfuehrung in die algebraische Geometrie,Verlag von Julius Springer,1973,A Chinese translation has been published by Science Press in China in 2008.
    [3]Weil A,Foundation of Algebraic Geometry,published by American Mathematical Society,1946and 1962.
    [4]Wang D K,Zero decomposition algorithms for system of polynomial equations,Proc.of the 4th Asian Symposium,Computer Mathematics,2000,67-70.
    [5]Chou S C,Schelter W F,and Yang J G,An algorithm for constructing gr?bner bases from characteristic sets and its application to geometry,Algorithmica,1990,5:147-154.
    [6]Wang D M,Irreducible decomposition of algebraic varieties via characteristic set and Gr?bner bases,Computer Aided Geometric Design,1992,9(6):471-484.