On Free Quotients of Complete Intersection Calabi-Yau Manifolds
Volker Braun
TL;DR
The paper addresses constructing non-simply connected Calabi–Yau threefolds by classifying free quotients of complete intersections in products of projective spaces (CICYs) via computer-aided analysis of ambient automorphisms. It develops a comprehensive framework of π-representations, projective-to-linear lifts (Schur/generalized Schur covers), and SymInd/AltInd operations to compute character-valued indices and prune the search without building explicit models. A Koszul-based equivariant cohomology approach yields closed-form index formulas, enabling efficient screening for freeness and smoothness; the authors implement the method with GAP/Singular and provide a public data set of free actions. The results enumerate all free actions up to the established bound, reveal structural properties of freely acting groups, and identify concrete quotients (including a three-generation model) with potential phenomenological relevance. The work advances systematic construction of non-simply connected Calabi–Yau manifolds and provides a practical toolkit for analyzing equivariant line bundles and quotient geometries.
Abstract
In order to find novel examples of non-simply connected Calabi-Yau threefolds, free quotients of complete intersections in products of projective spaces are classified by means of a computer search. More precisely, all automorphisms of the product of projective spaces that descend to a free action on the Calabi-Yau manifold are identified.