Flops for Complete Intersection Calabi-Yau Threefolds

TL;DR

This paper investigates the flops of Calabi-Yau threefolds realized as complete intersections in products of projective spaces, classifying their types, describing the resulting manifolds, and analyzing their properties and invariants.

Contribution

It classifies two types of flops for CICY Calabi-Yau threefolds based on configuration matrices and provides explicit descriptions and invariants for the resulting manifolds.

Findings

Second type of flop always yields isomorphic manifolds

First type of flop generally leads to non-isomorphic flops

Identification of infinite flop chains from configuration matrices

Abstract

We study flops of Calabi-Yau threefolds realised as Kaehler-favourable complete intersections in products of projective spaces (CICYs) and identify two different types. The existence and the type of the flops can be recognised from the configuration matrix of the CICY, which also allows for constructing such examples. The first type corresponds to rows containing only 1s and 0s, while the second type corresponds to rows containing a single entry of 2, followed by 1s and 0s. We give explicit descriptions for the manifolds obtained after the flop and show that the second type of flop always leads to isomorphic manifolds, while the first type in general leads to non-isomorphic flops. The singular manifolds involved in the flops are determinantal varieties in the first case and more complicated in the second case. We also discuss manifolds admitting an infinite chain of flops and show how to identify these from the configuration matrix. Finally, we point out how to construct the divisor images and Picard group isomorphisms under both types of flops.