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Results tagged with vector-bundles
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user 152391
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.
2
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0
answers
123
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Stability of cotangent bundle of hypersurface
Let $ X $ be a smooth hypersurface of degree $ d > 1 $ in $ \mathbb{P}^{n+1} $. What can be said about the stability (Slope/Gieseker) of the cotangent bundle of $ X $?
The closest reference I could fi …
- 936
2
votes
1
answer
393
views
Pullback of a vector bundle extension class
Let $ X $ be a variety with an automorphism $ \phi : X \rightarrow X $. Suppose there is a short exact sequence of vector bundles $ 0 \rightarrow F \rightarrow E \rightarrow G \rightarrow 0 $ on $ X $ …
- 936
2
votes
0
answers
326
views
The definition of the determinant of a coherent sheaf
Let $ X $ be a smooth (projective) variety and $ \mathcal{F} $ a torsion-free coherent sheaf of rank $ r $ on $ X $. The determinant $ \det \mathcal{F} $ can be defined by
(1) $ \det \mathcal F := ( \ …
- 936