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Results tagged with line-bundles
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user 5659
A continuously varying family of one-dimensional vector spaces over a topological space. A related tag is the vector-bundles tag.
4
votes
Technique to prove basepoint-freeness
I don't think that your assertion is true; for example, Lazarsfeld gives an example (PAG, 2.3.3) of a big and nef divisor on a surface such that its graded algebra is not finitely generated, so that t …
- 2,727
4
votes
Existence of a connection $A$ on a holomorphic line bundle $L$, s.t $F(A)=(\deg L)\omega$
Let $h_0$ be any hermitian metric on $L$, with curvature $F(h_0)$.
By Hodge theory, there exists a function $f\in \mathcal C^{\infty}(X)$ such that
$$\Delta_{\omega} f =\Lambda_{\omega} F(h_0) - \ma …
- 2,727