Computational Tools for Cohomology of Toric Varieties
Ralph Blumenhagen, Benjamin Jurke, Thorsten Rahn
TL;DR
This paper reviews innovative computational methods for calculating cohomology classes on toric varieties, emphasizing an algorithm implemented in cohomCalg and its applications in string theory model analysis.
Contribution
It introduces a novel algorithm for computing line-bundle cohomology on toric varieties and demonstrates its application in string compactification models.
Findings
Effective algorithm for cohomology computation implemented in cohomCalg
Application to (0,2) heterotic string models
Utility demonstrated on a new target space dual pair
Abstract
In this review, novel non-standard techniques for the computation of cohomology classes on toric varieties are summarized. After an introduction of the basic definitions and properties of toric geometry, we discuss a specific computational algorithm for the determination of the dimension of line-bundle valued cohomology groups on toric varieties. Applications to the computation of chiral massless matter spectra in string compactifications are discussed and, using the software package cohomCalg, its utility is highlighted on a new target space dual pair of (0,2) heterotic string models.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.