Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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THE CAYLEY-BACHARACH THEOREM VIA TRUNCATED MOMENT PROBLEMS

  • Yoo, Seonguk (Department of Mathematics Education and RINS, Gyeongsang National University)
  • Received : 2021.08.02
  • Accepted : 2021.12.16
  • Published : 2021.12.30
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Abstract

The Cayley-Bacharach theorem says that every cubic curve on an algebraically closed field that passes through a given 8 points must contain a fixed ninth point, counting multiplicities. Ren et al. introduced a concrete formula for the ninth point in terms of the 8 points [4]. We would like to consider a different approach to find the ninth point via the theory of truncated moment problems. Various connections between algebraic geometry and truncated moment problems have been discussed recently; thus, the main result of this note aims to observe an interplay between linear algebra, operator theory, and real algebraic geometry.

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Acknowledgement

The author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2020R1F1A1A01070552).

References

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  4. Q. Ren, J. Richter-Gebert, and B. Sturmfels,Cayley-Bacharach Formulas, The American Mathematical Monthly, 122 (9) (2015), 845-854 https://doi.org/10.4169/amer.math.monthly.122.9.845
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