On the geometry of the higher dimensional Voisin maps

Chenyu Bai

On the geometry of the higher dimensional Voisin maps

Algebraic Geometry 2024-05-28 v2

Authors: Chenyu Bai

Abstract

Voisin constructed self-rational maps of Calabi-Yau manifolds obtained as varieties of $r$ -planes in cubic hypersurfaces of adequate dimension. This map has been thoroughly studied in the case $r=1$ , which is the Beauville-Donagi case. In this paper, we compute the action of $\Psi$ on holomorphic forms for any $r$ . For $r=2$ , we compute the action of $\Psi$ on the Chow group of $0$ -cycles, and confirm that it is as expected from the generalized Bloch conjecture.

Keywords

Voisin maps Calabi-Yau manifolds cubic hypersurfaces holomorphic forms Chow group generalized Bloch conjecture

Cite

@article{arxiv.2404.10138,
  title  = {On the geometry of the higher dimensional Voisin maps},
  author = {Chenyu Bai},
  journal= {arXiv preprint arXiv:2404.10138},
  year   = {2024}
}

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