Geometry and Topology of String Junctions

Journal of Singularities
volume 15 (2016), 36-52

Received: 24 October 2014. Received in revised form: 4 March 2015.

DOI: 10.5427/jsing.2016.15c

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Abstract:

We study elliptic fibrations by analyzing suitable deformations of the fibrations and vanishing cycles. We introduce geometric string junctions and describe some of their properties. We show how the geometric string junctions manifest the structure of the Lie algebra of the Dynkin diagrams associated to the singularities of the elliptic fibration. One application in physics is in F-theory, where our novel approach connecting deformations and Lie algebras describes the structure of generalized type IIB seven-branes and string junction states which end on them.