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