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Results tagged with vector-bundles
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user 136084
A continuously varying family of vector spaces of the same dimension over a topological space. If the vector spaces are one-dimensional, the term line bundle is used and has the associated tag line-bundles.
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Stable extensions by line bundles on Riemann surfaces
Let $C$ be a (complex irreducible) curve of genus at least two. Then, for every line bundle $L$ on $C$ of negative degree, there exist extensions of $L^{-1}$ by $L$ which are stable. Furthermore, the …
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Surfaces with $\Omega_X$ big are of general type
Given a complete algebraic variety $X$ over $\mathbb{C}$ and a vector bundle $E$ of rank $r$, let $\Omega(X,E)$ denote the graded ring $\bigoplus_{m\ge 0}H^0(X,S^mE)$, and define $$\lambda(E,X)=\oper …
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