= Monomial curve
{title2=$\operatorname{Spec}k[t^{a_1},\ldots,t^{a_n}]$}
Over a <field> $k$, an affine curve parametrized by positive integer powers of one parameter. Its coordinate <ring> is the subalgebra generated by those powers, and its defining <prime ideal> is the kernel of $k[x_1,\ldots,x_n]\to k[t]$ sending $x_i$ to $t^{a_i}$. Equal exponent sums yield binomial relations. Studying those relations connects an additive semigroup of exponents to the geometry of the curve.
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