L. B. Anderson

 A. Constantin

J. Gray

Y. He

S. Lee

A. Lukas

We introduce CIPro, a new toolkit that automates calculations on Calabi–Yau geometries and helps explore string compactifications and vacua.

Complete intersections and line bundles over products of projective spaces underpin many string compactifications. We present CIPro, a Mathematica package that computes Chern classes, Hilbert series, bundle cohomology, symmetries and Gopakumar–Vafa invariants. In addition, CIPro brings together key Calabi–Yau data sets, giving researchers a toolkit for exploring heterotic, Type II and other compactification geometries.

CIPro is a Mathematica package for constructing and analyzing complete intersections in products of projective spaces and line bundles over such varieties. It computes properties of complete intersections, such as Chern classes, Hilbert series, GV invariants and symmetries, as well as properties of line bundles on complete intersections, including their cohomology groups. The package also consolidates a number of data sets available in the literature into a single system, including the lists of complete intersection Calabi-Yau three- and four-folds. This short tutorial introduces the package, provides a brief discussion of some of the mathematical background underlying its computations, and gives a series of examples to illustrate its use. These tools are of utility for many computations in string compactifications, especially for Calabi-Yau geometries appearing in Heterotic and Type II constructions. Many tools apply beyond the Calabi-Yau context, including for example, almost Fano bases in F-theory.

A Calabi–Yau toolkit

CIPro package: complete intersections in products of projective spaces and line bundles