On the existence of almost Fano threefolds with del Pezzo fibrations

TL;DR

This paper constructs explicit examples of almost Fano threefolds with del Pezzo fibrations for 10 classes where their existence was previously unproven, completing the classification.

Contribution

It provides the first explicit constructions of almost Fano threefolds with del Pezzo fibrations for the remaining 10 unverified classes.

Findings

Constructed examples for all 10 previously unproven classes.

Confirmed the existence of these threefolds in each class.

Contributed to the classification of almost Fano threefolds with del Pezzo fibrations.

Abstract

By Jahnke-Peternell-Radloff and Takeuchi, almost Fano threefolds with del Pezzo fibrations were classified. Among them, there exists 10 classes such that the existence of members of these was not proved. In this paper, we construct such examples belonging to each of 10 classes.