We prove that the Cox ring of the blowing-up of a minimal toric surface of Picard rank two is finitely generated. As part of our proof of this result we provide a necessary and sufficient condition for finite generation of Cox rings of normal projective -factorial surfaces.
Laface, A., Ugaglia, L. (2025). On Blowing Up Minimal Toric Surfaces. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2025(6) [10.1093/imrn/rnaf052].
On Blowing Up Minimal Toric Surfaces
Ugaglia, Luca
2025-03-01
Abstract
We prove that the Cox ring of the blowing-up of a minimal toric surface of Picard rank two is finitely generated. As part of our proof of this result we provide a necessary and sufficient condition for finite generation of Cox rings of normal projective -factorial surfaces.
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