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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

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From first-order deformation to complex deformation of a pair $(X,L)$

$\DeclareMathOperator\Spec{Spec}$Let $L \rightarrow X$ be an ample line bundle over $X$ which is a compact complex manifold. Suppose that I have a first-order deformation of the pair $(X,L)$. When doe …
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