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Results tagged with coherent-sheaves
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user 152391
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
4
votes
0
answers
503
views
Does a torsion-free coherent sheaf embed into a locally free sheaf?
Let $ X $ be a Noetherian integral regular scheme and $ \mathcal{F} $ be a torsion-free coherent sheaf. (One definition of torsion-free is that the natural map $ \mathcal{F} \rightarrow \mathcal{F} \o …
- 936
3
votes
0
answers
234
views
Stability and simplicity of tangent sheaf of Grassmannian
Everything is over the complex numbers. Let $ X = \text{Gr}(k,n) $ be a Grassmannian variety and with tangent sheaf $ T_X $.
(1) Is $ T_X $ simple, i.e. is $\text{Hom} ( T_X, T_X) = \mathbb{C} $?
(2 …
- 936