Classification of Mukai pairs with dimension $4$ and rank $2$

Akihiro Kanemitsu

Classification of Mukai pairs with dimension $4$ and rank $2$

Algebraic Geometry 2018-06-21 v1

Authors: Akihiro Kanemitsu

Abstract

We give the complete classification of Mukai pairs of dimension $4$ and rank $2$ with Picard number one, that is, pairs $(X,E)$ where $X$ is a Fano $4$ -fold with Picard number one, and $E$ is an ample vector bundle of rank two on $X$ with $c_1(X) = c_1(E)$ . Equivalently, the present paper completes the classification of ruled Fano $5$ -folds with index two, which was partially done by C. Novelli and G. Occhetta in 2007.

Keywords

Mukai pairs Fano varieties vector bundles Picard number classification ruled Fano folds

Cite

@article{arxiv.1806.07587,
  title  = {Classification of Mukai pairs with dimension $4$ and rank $2$},
  author = {Akihiro Kanemitsu},
  journal= {arXiv preprint arXiv:1806.07587},
  year   = {2018}
}

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23 pages

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