Mordell-Weil Torsion and the Global Structure of Gauge Groups in F-theory

Understand

We study the global structure of the gauge group $G$ of F-theory compactified on an elliptic fibration $Y$.

• The global properties of $G$ are encoded in the torsion subgroup of the Mordell-Weil group of rational sections of $Y$.
• Generalising the Shioda map to torsional sections we construct a specific integer divisor class on $Y$ as a fractional linear combination of the resolution divisors associated with the Cartan subalgebra of $G$.
• This divisor class can be interpreted as an element of the refined coweight lattice of the gauge group.