English

Full exceptional collections on Fano threefolds and groups generated by spherical twists on K3 surfaces

Algebraic Geometry 2026-02-16 v4

Abstract

For a Fano threefold admitting a full exceptional collection of vector bundles of length four we show that all full exceptional collections consist of shifted vector bundles. We prove this via a detailed study of the group generated by spherical twists on an anticanonical divisor. For example, we prove that this group is free and provide explicit generators.

Keywords

Cite

@article{arxiv.2412.06023,
  title  = {Full exceptional collections on Fano threefolds and groups generated by spherical twists on K3 surfaces},
  author = {Anya Nordskova and Michel Van den Bergh},
  journal= {arXiv preprint arXiv:2412.06023},
  year   = {2026}
}

Comments

Corrected ERC funding acknowledgement