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Journal of Systems Science and Complexity

, Volume 32, Issue 1, pp 47–61 | Cite as

Hilbert Problem 15 and Ritt-Wu Method (I)

  • Banghe LiEmail author
Article

Abstract

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.

Keywords

Cubed curves with cusp Hilbert Problem 15 Ritt-Wu Method 

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Notes

Acknowledgements

The author thanks professor Dingkang WANG for many helps deeply

References

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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.KLMM, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina

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