MathOverflow Asked on January 5, 2022
Let $P$ be a prime ideal in $S=mathbb{C}[x_1,ldots , x_n],$ and write $[n] = { 1, ldots , n }.$ The algebraic matroid of $P$ can be defined according to circuit axioms as follows: $Csubset [n]$ is a circuit if $P cap mathbb{C} [x_i mid i in C]$ is principal, and we call a generator of this ideal a circuit polynomial. The circuit ideal $P_{mathcal{C}}subset S$ is generated by all circuit polynomials.
Question For which $P$ do we have $sqrt{P_{mathcal{C}}}=P$?
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