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