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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 ...
Han Jin Ma's user avatar
2 votes
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On spin structure for Kähler manifolds and square roots of $\det (TX)$

I'm stuck on the proof that for a (compact) Kähler manifold $X$ (of complex dimension $n$), a spin structure on the tangent bundle $TX$ is equivalent to a line bundle $L$ together with an isomorphism $...
Alessandro Nanto's user avatar
1 vote
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Compact complex manifolds with nef canonical bundle have nonnegative Kodaira dimension

Let $X$ be a compact Kähler manifold with nef canonical bundle. The (Kähler extension of the) abundance conjecture asserts that $K_X$ is semi-ample, and thus $K_X^{\otimes m}$ admits a section for ...
ABBC's user avatar
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