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The Cayley?Bacharach theorem says that every cubic curve on an al- gebraically 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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참고문헌 (6)
참고문헌 신청
M. Chasles / 1885 / Trait_e des sections coniques / Gauthier-Villars
R. Curto / 1996 / Solution of the truncated complex moment problem with at data / Memoirs Amer. Math. Soc (568)
D. Eisenbud / 1996 / Cayley-Bacharach theorems and conjectures / Bull. Amer. Math. Soc 33(3):295~324
Q. Ren / 2015 / Cayley-Bacharach Formulas / The American Math-ematical Monthly 122(9):845~854
J. L. Smul'jan / 1959 / An operator Hellinger integral(Russian) / Mat. Sb 91:381~430
R. Curto / 1996 / Solution of the truncated complex moment problem with at data / Memoirs Amer. Math. Soc (568)
D. Eisenbud / 1996 / Cayley-Bacharach theorems and conjectures / Bull. Amer. Math. Soc 33(3):295~324
Q. Ren / 2015 / Cayley-Bacharach Formulas / The American Math-ematical Monthly 122(9):845~854
J. L. Smul'jan / 1959 / An operator Hellinger integral(Russian) / Mat. Sb 91:381~430
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