Determinantal ideals and monomial curves in the three-dimensional space

Mathematics – Algebraic Geometry

Scientific paper

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Scientific paper

10.1142/S0219498807002272

We show that the defining ideal of every monomial curve in the affine or
projective three-dimensional space can be set-theoretically defined by three
binomial equations, two of which set-theoretically define a determinantal ideal
generated by the 2-minors of a $2\times 3$ matrix with monomial entries.

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