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Tagged with line-bundles flag-varieties
3 questions
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Restriction of a line bundle on $G/B$ to a fibre which is isomorphic to $\mathbb{P}^1$
Let $G$ be a reductive group over a field $k$ of characteristic zero with maximal split torus $T$, Borel $B \supset T$ and Weyl group $W$. Set $X:=G/B$ and $C_w:=BwB/B \subset X$ for $w \in W$ the ...
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Character which defines canonical bundle on flag variety
Let $G$ be a reductive group over a field $k$ of characteristic zero with maximal split torus $T$ and Borel $B \supset T$ defining a set of simple roots $\Delta$. Additionally let $\rho$ be the half ...
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How the existence of holomorphic sections depends on the choice of complex structure
In this Mathoverflow question it is asked how many invariant complex structures exist on the full flag manifold of $SU(m)$. In this question it is asked when a line bundle over a flag manifold has ...