Lefschetz fibrations on adjoint orbits - PMA

<strong>Lefschetz</strong> <strong>fibrations</strong> via Lie theory
Notation/definition:
Let g be a complex semisimple Lie algebra and G a connected Lie
group with Lie algebra g.
The Cartan–Killing form of g,
〈X , Y 〉 = tr (ad (X ) ad (Y )) ∈ C
is symmetric and nondegenerate.
Fix a Cartan subalgebra h ⊂ g. A root of h is a linear functional
α : h → C, α = 0. Denote the set of all roots by Π.
An element H ∈ h is regular if α (H) = 0 for all α ∈ Π.
Elizabeth Gasparim <strong>Lefschetz</strong> <strong>fibrations</strong> on adjoint orbits