An inductive approach to generalized abundance using nef reduction

Priyankur Chaudhuri

An inductive approach to generalized abundance using nef reduction

Algebraic Geometry 2022-09-12 v3

Authors: Priyankur Chaudhuri

Abstract

We use the canonical bundle formula for parabolic fibrations to give an inductive approach to the generalized abundance conjecture using nef reduction. In particular, we observe that generalized abundance holds for a klt pair $(X,B)$ if the nef dimension $n(K_X+B+L)=2$ and $K_X+B \geq 0$ or $n(K_X+B+L)=3$ and $\kappa(K_X+B )>0$ .

Keywords

nef and ample line bundles

Cite

@article{arxiv.2110.10252,
  title  = {An inductive approach to generalized abundance using nef reduction},
  author = {Priyankur Chaudhuri},
  journal= {arXiv preprint arXiv:2110.10252},
  year   = {2022}
}

Comments

7 pages, this version corrects an error in the previous one

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