On the Simultaneously Generation of Jets of the Adjoint Bundles

2017/09/19 by Shentu, Junchao, Zhang, Yongming
#14C20 #14E25 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.06373

Abstract

In this paper, we investigate the problem of simultaneously generations of r-jets of ω_X⊗ L^{⊗ m} when L is ample and base point free. It turns out that in this case, the bound of m is optimistic, i.e. m≥ f(r)=n+r+1, which is linear in r. Our results work over arbitrary characteristics. We also treat the same problem when X is singular where ω_X is replaced by the pushforward of canonical sheaves or the cohomology sheaves of dualizing complexes.

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