Bulletin of the
Korean Mathematical Society BKMS

Sextic moment problems with an infinite algebraic variety are still widely open. We study the problem with a single cubic column relation associated to 3 parallel lines in which the variety is infinite. It turns out that this specific column relation has a strong connection with moment problems that have a symmetric algebraic variety. We present more concrete solutions to some sextic moment problems with a symmetric variety.

Keywords: truncated moment problems, symmetric algebraic variety, consistency, rank-one decomposition

MSC numbers: Primary 44A60, 47A57; Secondary 11P70, 15-04, 47A20, 32A60