By Vincenzo Di Gennaro
We express a pointy Castelnuovo sure for the i-th plurigenus of a soft number of given size n and measure d within the projective house P r , and classify the types achieving the certain, while n2, r2n+1, d>>r and i>>r. whilst n=2 and r=5, or n=3 and r=7, we provide an entire class, i.e. for any i1. occasionally, the types with maximal plurigenus usually are not Castelnuovo types, i.e. types with maximal geometric genus. for instance, a Castelnuovo type whole intersection on quite a few size n+1 and minimum measure in P r , with r>(n 2 +3n)/(n-1), has no longer maximal i-th plurigenus, for i>>r. on account of the certain at the plurigenera, we receive an higher sure for the self-intersection of the canonical package deal of a soft projective style, whose canonical package deal is gigantic and nef.
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