On the direct image of the adjoint line bundle

Indranil Biswas; Fatima Laytimi; D. S. Nagaraj; Werner Nahm

On the direct image of the adjoint line bundle

Algebraic Geometry 2023-10-05 v1

Authors: Indranil Biswas , Fatima Laytimi , D. S. Nagaraj , Werner Nahm

Abstract

We give an algebraic-geometric proof of the fact that for a smooth fibration $\pi: X \longrightarrow Y$ of projective varieties, the direct image $\pi_*(L\otimes K_{X/Y})$ of the adjoint line bundle of an ample (respectively, nef and $\pi$ -strongly big) line bundle $L$ is ample (respectively, nef and big).

Keywords

adjoint line bundle direct image smooth fibration projective varieties ample line bundle nef and big

Cite

@article{arxiv.2310.02764,
  title  = {On the direct image of the adjoint line bundle},
  author = {Indranil Biswas and Fatima Laytimi and D. S. Nagaraj and Werner Nahm},
  journal= {arXiv preprint arXiv:2310.02764},
  year   = {2023}
}

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