Cohomology of Line Bundles: A Computational Algorithm

TL;DR

This paper introduces a computational algorithm for calculating line bundle cohomology on toric varieties, crucial for string theory compactification models involving complex manifolds and vector bundles.

Contribution

It provides a novel algorithmic approach to compute line bundle cohomology, facilitating advanced studies in string compactifications.

Findings

Algorithm efficiently computes cohomology classes.

Applicable to complete intersection manifolds in toric varieties.

Supports analysis of massless modes in string theory models.

Abstract

We present an algorithm for computing line bundle valued cohomology classes over toric varieties. This is the basic starting point for computing massless modes in both heterotic and Type IIB/F-theory compactifications, where the manifolds of interest are complete intersections of hypersurfaces in toric varieties supporting additional vector bundles.