The Cox Ring of a Del Pezzo Surface¶
Batyrev, V. V., & Popov, O. N. The Cox Ring of a Del Pezzo Surface.
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1 citation across 1 artifact.
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Domain-specific¶
- Mori dream space
- Not synonymous with a toric variety. Smooth toric projective examples qualify under Hu and Keel's hypotheses, but the degree-five del Pezzo surface $X_4$ provides a non-toric Mori dream space through its finitely generated, non-polynomial Cox ring.
This sourceSection 2, Theorem 3.2 and Proposition 4.1. The Cox-ring/Grassmannian identification does not identify the surface with the Grassmannian.
- Not synonymous with a toric variety. Smooth toric projective examples qualify under Hu and Keel's hypotheses, but the degree-five del Pezzo surface $X_4$ provides a non-toric Mori dream space through its finitely generated, non-polynomial Cox ring.
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