On the Cox ring of $\mathbf{P}^2$ blown up in points on a line

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We show that the blow-up of

$\mathbf{P}^2$ in

$n$ points on a line has finitely generated Cox ring. We give explicit generators for the ring and calculate its defining ideal of relations.

2011-09-01

Ottem, J. C. (2011). On the Cox ring of

$\mathbf{P}^2$ blown up in points on a line. MATHEMATICA SCANDINAVICA, 109(1), 22–30. https://doi.org/10.7146/math.scand.a-15175

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