Twistor geometry of the Flag manifold

A study is made of algebraic curves and surfaces in the flag manifold $$\mathbb {F}=SU(3)/T^2$$ , their configuration relative to twistor projection $$\pi $$ from {F}$$ complex projective plane {P}^{2}$$ defined with help an anti-holomorphic involution $$j$$ . This motivated by analogous studies low degree space {P}^3$$ 4-dimensional sphere $$S^4$$ Deformations fibers project real whose metric geometry investigated. Attention then focussed on toric del Pezzo that are simplest type bidegree $$(1,1)$$ These define orthogonal structures specified dense open subsets its Fubini-Study metric. The discriminant loci various determined, bounds given number contained more general