Projections of del Pezzo surfaces and Calabi--Yau threefolds

TL;DR

This paper investigates the syzygetic structure of projected del Pezzo surfaces to construct and smooth singular Calabi-Yau threefolds, resulting in new examples with Picard rank 1 and illustrating a primitive contraction with a specific exceptional divisor.

Contribution

It introduces a novel method of constructing Calabi-Yau threefolds via projections of del Pezzo surfaces and analyzes their geometric properties, including primitive contractions.

Findings

New Calabi-Yau threefold examples with Picard rank 1

Explicit construction of a primitive contraction with a specific exceptional divisor

Insights into the syzygetic structure of projected del Pezzo surfaces

Abstract

We study the syzygetic structure of projections of del Pezzo surfaces in order to construct singular Calabi-Yau threefolds. By smoothing those threefolds, we obtain new examples of Calabi-Yau threefolds with Picard group of rank 1. We also give an example of type II primitive contraction whose exceptional divisor is the blow-up of the projective plane at a point.