By Vincenzo Di Gennaro
We convey a pointy Castelnuovo sure for the i-th plurigenus of a tender number of given measurement n and measure d within the projective area P r , and classify the types reaching the sure, whilst n2, r2n+1, d>>r and i>>r. while n=2 and r=5, or n=3 and r=7, we supply an entire class, i.e. for any i1. every now and then, the kinds with maximal plurigenus aren't Castelnuovo kinds, i.e. types with maximal geometric genus. for instance, a Castelnuovo type entire intersection on a number of size n+1 and minimum measure in P r , with r>(n 2 +3n)/(n-1), has now not maximal i-th plurigenus, for i>>r. on account of the sure at the plurigenera, we receive an higher sure for the self-intersection of the canonical package deal of a delicate projective sort, whose canonical package deal is enormous and nef.
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A bound on the plurigenera of projective varieties by Vincenzo Di Gennaro