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Results tagged with vector-bundles
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user 44860
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.
8
votes
Accepted
If the restriction of a vector bundle to a divisor is semi stable, then is the vector bundle...
First of all, as Allen Knutson remarks, $X$ should have dimension at least two.
Now the Mehta-Ramanathan theorem tells you that if $\mathcal E$ is $H$-semistable and $D \in |mH|$ is general, with $m$ …
- 1,072
7
votes
Accepted
Why do we need ampleness in the definition of stability/semistability
You are right, the condition that $L$ be ample can be weakened. In fact, on an $n$-dimensional normal projective variety $X$ one can measure (semi-)stability with respect to an arbitrary movable curve …
- 1,072