On K3 fibred Calabi-Yau threefolds in weighted scrolls

TL;DR

This paper classifies certain mildly singular Calabi-Yau threefolds fibred in weighted K3 surfaces within weighted scrolls, extending previous classifications and exploring degenerations and embeddings.

Contribution

It extends the classification of Calabi-Yau threefolds fibred in weighted K3 surfaces and investigates their degenerations and embeddings into weighted scrolls.

Findings

Classification of mildly singular Calabi-Yau threefolds in weighted scrolls

Analysis of projective degenerations of these threefolds

Discussion on embedding projective fibrations into weighted scrolls

Abstract

The aim of this paper is to classify mildly singular Calabi-Yau threefolds fibred in low-degree weighted K3 surfaces and embedded as anticanonical hypersurfaces in weighted scrolls, extending results of Mullet. We also study projective degenerations, revisiting an example due to Gross and Ruan. Finally we briefly discuss the general question of embedding a projective fibration into a weighted scroll.