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Results tagged with line-bundles
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user 4096
A continuously varying family of one-dimensional vector spaces over a topological space. A related tag is the vector-bundles tag.
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canonical model of a reducible curve
Let $C$ be a stable reducible curve. Is there a natural way to define it's canonical model (I guess via the dualizing sheaf)? And does somehow the dualizing sheaf restrict to the (probably twisted) ca …
- 3,779
2
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Accepted
On morphisms to projective space arising from a linear system
$E$ can't intersect $C$ in a finite number of points because otherwise the restriction of $\phi$ to $C$ would be a finite degree morphism, which you assume is not. $E$ is the pull-back of the hyperpla …
- 3,779
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How can one check that two line bundles on $\overline{M}_{0,n}$ coincide?
Let $X$ be the Deligne-Mumford compactification of $\mathcal{M}_{0,n}$. Suppose I have two (big) line bundles $L$ and $L'$ on $X$ and that I want to show that they are the same element of $Pic(X)$. Of …
- 3,779
1
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Does the semi-stable set determine the linearization of a GIT quotient?
Suppose I have a morphism $f:X\to Y$ which is a GIT quotient of $X$ with respect to some reductive, linear group.
Does the semistable $X^{ss}$ and stable locus $X^s\subset X$ determine completely the …
- 3,779