Hilbert schemes of some threefold scrolls over 𝔽 _e

Abstract

Hilbert schemes of suitable smooth, projective threefold scrolls over the Hirzebruch surface 𝔽

An unbounded family of log Calabi–Yau pairs

“…where C 0 is the unique effective divisor on F n such that C 2 0 = −n and F is the class of the fiber with respect to the P 1 -bundle structure on F n . For any n denote by X the scroll defined as P(V), the projective bundle of hyperplanes in V. For futher information about these scrolls, see, for instance, [FF15]. If the linear system | − 2K X | had a smooth member, then the double covering of X -branched along it -would be a smooth Calabi-Yau manifold.…”