Korean J. Math. Vol. 29 No. 4 (2021) pp.741-747
DOI: https://doi.org/10.11568/kjm.2021.29.4.741

The Cayley-Bacharach theorem via truncated moment problems

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Seonguk Yoo


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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Supporting Agencies

National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT)


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