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New Examples and Non-examples of Mori Dream Spaces when Blowing up Toric Surfaces
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We study the question of whether the blow-ups of toric surfaces of Picard number one at the identity point of the torus are Mori Dream Spaces. For some of these toric surfaces, the question whether the blow-up is a Mori Dream Space is equivalent to countably many planar interpolation problems. We state a conjecture which generalizes a theorem of Gonzalez and Karu. We give new examples and non-examples of Mori Dream Spaces among these blow-ups.
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Infinitely generated symbolic Rees rings of positive characteristic
For the ideal I generated by the 2-minors of the matrix {{x^7, y^2, z}, {y^11, z, x^10}}, the extended symbolic Rees ring is Noetherian if and only if the field has characteristic 2 or 3.
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