On Calabi-Yau generalized complete intersections from Hirzebruch varieties and novel K3-fibrations

TL;DR

This paper explores the construction of generalized complete intersection Calabi-Yau three-folds, revealing new elliptic and K3-fibrations involving Hirzebruch surfaces and extending cohomology computation methods.

Contribution

It introduces a generalized framework for constructing Calabi-Yau varieties with negative degrees, discovering new fibrations and extending cohomology techniques.

Findings

Identified sequences of novel Calabi-Yau three-folds with elliptic and K3-fibrations.

Extended cohomology computation methods to generalized complete intersections.

Discovered new manifolds involving Hirzebruch surfaces.

Abstract

We consider the construction of Calabi-Yau varieties recently generalized to where the defining equations may have negative degrees over some projective space factors in the embedding space. Within such "generalized complete intersection" Calabi-Yau ("gCICY") three-folds, we find several sequences of distinct manifolds. These include both novel elliptic and K3-fibrations and involve Hirzebruch surfaces and their higher dimensional analogues. En route, we generalize the standard techniques of cohomology computation to these generalized complete intersection Calabi-Yau varieties.