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Weighted Hypersurfaces with Either Assigned Volume or Many Vanishing Plurigenera

Weighted Hypersurfaces with Either Assigned Volume or Many Vanishing Plurigenera

In this article, we construct, for every n, smooth varieties of general type of dimension n with the first plurigenera equal to zero. Hacon-McKernan, Takayama, and Tsuji have recently shown that there are numbers r n such that ∀ r ≥ r n , the r − canonical map of …