On the motive of codimension 2 linear sections of $\hbox{Gr}(3,6)$

Robert Laterveer

On the motive of codimension 2 linear sections of $\hbox{Gr}(3,6)$

Algebraic Geometry 2021-05-17 v1

Authors: Robert Laterveer

Abstract

We consider Fano sevenfolds $Y$ obtained by intersecting the Grassmannian $\hbox{Gr}(3,6)$ with a codimension 2 linear subspace (with respect to the Pl\"ucker embedding). We prove that the motive of $Y$ is Kimura finite-dimensional. We also prove the generalized Hodge conjecture for all powers of $Y$ .

Keywords

grassmannian linear section motive kimura finite-dimensional generalized hodge conjecture fano variety

Cite

@article{arxiv.2105.06856,
  title  = {On the motive of codimension 2 linear sections of $\hbox{Gr}(3,6)$},
  author = {Robert Laterveer},
  journal= {arXiv preprint arXiv:2105.06856},
  year   = {2021}
}

Comments

11 pages, to appear in Tokyo J. Math., comments welcome. arXiv admin note: text overlap with arXiv:2009.11061, arXiv:2105.03171

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