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Register a new userOn blowing up the weighted projective plane
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We investigate the blow-up of a weighted projective plane at a general point. We provide criteria and algorithms for testing if the result is a Mori dream surface and we compute the Cox ring in several cases. Moreover applications to the study of $overline{M}_{0,n}$ are discussed.
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In this paper, we first introduce geometric operations for linear categories, and as a consequence generalize Orlovs blow up formula [O04] to possibly singular local complete intersection centres. Second, we introduce refined blowing up of linear category along base--locus, and show that this operation is dual to taking linear section. Finally, as an application we produce examples of Calabi--Yau manifolds which admits Calabi--Yau categories fibrations over projective spaces.
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