Characteristic numbers of elliptic fibrations with non-trivial Mordell-Weil groups

Abstract

We compute characteristic numbers of elliptically fibered fourfolds with multisections or non-trivial Mordell-Weil groups. We first consider the models of type E${}_{9-d}$ with $d=1,2,3,4$ whose generic fibers are normal elliptic curves of degree $d$. We then analyze the characteristic numbers of the $Q_7$-model, which provides a smooth model for elliptic fibrations of rank one and generalizes the E${}_5$, E${}_6$, and E${}_7$-models. Finally, we examine the characteristic numbers of $G$-models with $G=\text{SO}(n)$ with $n=3,4,5,6$ and $G=\text{PSU}(3)$ whose Mordell-Weil groups are respectively $\mathbb{Z}/2\mathbb{Z}$ and $\mathbb{Z}/3\mathbb{Z}$. In each case, we compute the Chern and Pontryagin numbers, the Euler characteristic, the holomorphic genera, the Todd-genus, the L-genus, the A-genus, and the eight-form curvature invariant from M-theory.

23 pages, 14 Tables. arXiv admin note: text overlap with arXiv:1807.08755

References in corpus (4)

• F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches
• A New Model for Elliptic Fibrations with a Rank One Mordell-Weil Group: I. Singular Fibers and Semi-Stable Degenerations
• M-theory on Elliptic Calabi-Yau Threefolds and 6d Anomalies
• Mordell-Weil Torsion, Anomalies, and Phase Transitions

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• F-theory models with 3 to 8 U(1) factors on K3 surfaces
• The suspended pinch point and SU($2$)$\times$U($1$) gauge theories
• Matter representations from geometry: under the spell of Dynkin
• Flops and Fibral Geometry of E${}_7$-models