an:06853676
Zbl 1383.83147
Anderson, Lara B.; Gao, Xin; Gray, James; Lee, Seung-Joo
Fibrations in CICY threefolds
EN
J. High Energy Phys. 2017, No. 10, Paper No. 77, 63 p. (2017).
00377836
2017
j
83E30 14J32 32Q25 81T30 53B35
differential and algebraic geometry; F-theory; superstring vacua
Summary: In this work we systematically enumerate genus one fibrations in the class of 7,890 Calabi-Yau manifolds defined as complete intersections in products of projective spaces, the so-called CICY threefolds. This survey is independent of the description of the manifolds and improves upon past approaches that probed only a particular algebraic form of the threefolds (i.e. searches for ``obvious'' genus one fibrations as in [\textit{J. Gray} et al., ``Topological invariants and fibration structure of complete intersection Calabi-Yau four-folds'', Preprint, \url{arXiv:1405.2073}] and [\textit{L. B. Anderson} et al., ``Multiple fibrations in Calabi-Yau geometry and string dualities'', Preprint, \url{arXiv:1608.07555}]). We also study K3-fibrations and nested fibration structures. That is, K3 fibrations with potentially many distinct elliptic fibrations. To accomplish this survey a number of new geometric tools are developed including a determination of the full topology of all CICY threefolds, including triple intersection numbers. In 2, 946 cases this involves finding a new ``favorable'' description of the manifold in which all divisors descend from a simple ambient space. Our results consist of a survey of obvious fibrations for all CICY threefolds and a complete classification of all genus one fibrations for 4,957 ``K??hler favorable'' CICYs whose K??hler cones descend from a simple ambient space. Within the CICY dataset, we find 139,597 obvious genus one fibrations, 30,974 obvious K3 fibrations and 208,987 nested combinations. For the K??hler favorable geometries we find a complete classification of 377,559 genus one fibrations. For one manifold with Hodge numbers (19, 19) we find an explicit description of an infinite number of distinct genus-one fibrations extending previous results for this particular geometry that have appeared in the literature. The data associated to this scan is available in [\url{http://www1.phys.vt.edu/cicydata/}].
Reviewer (Berlin)