Flops, Gromov-Witten Invariants and Symmetries of Line Bundle Cohomology on Calabi-Yau Three-folds

TL;DR

This paper explores how zeroth line bundle cohomology on Calabi-Yau three-folds reveals flop transitions, Gromov-Witten invariants, and symmetries, using examples of Picard number 2 complete intersection manifolds.

Contribution

It demonstrates the relationship between cohomology, flop transitions, and symmetries on the Picard lattice in specific Calabi-Yau three-folds.

Findings

Zeroth cohomology encodes flop transitions and Gromov-Witten invariants.

Identifies symmetries preserving zeroth cohomology on Picard lattices.

Provides explicit examples of Calabi-Yau three-folds with these properties.

Abstract

The zeroth line bundle cohomology on Calabi-Yau three-folds encodes information about the existence of flop transitions and the genus zero Gromov-Witten invariants. We illustrate this claim by studying several Picard number 2 Calabi-Yau three-folds realised as complete intersections in products of projective spaces. Many of these manifolds exhibit certain symmetries on the Picard lattice which preserve the zeroth cohomology.