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I have a very easy question, which I couldn't get in the literature. Please forgive me if it is so easy!!! Question: Is a stable vector bundle over a curve $C$ is projective (as a $\mathcal O_C$-module) ? is it injective? Could you give me a reference?

One may ask a further question: in which cases a locally free sheaf is projective (resp. injective)?

Thanks

I have a very easy question, which I couldn't get in the literature. Please forgive me if it is so easy!!! Question: Is a stable vector bundle over a curve $C$ is projective (as a $\mathcal O_C$-module) ? is it injective? Could you give me a reference?

Thanks

I have a very easy question, which I couldn't get in the literature. Please forgive me if it is so easy!!! Question: Is a stable vector bundle over a curve $C$ is projective (as a $\mathcal O_C$-module) ? is it injective? Could you give me a reference?

One may ask a further question: in which cases a locally free sheaf is projective (resp. injective)?

Thanks

Source Link
Z.A.Z.Z
Z.A.Z.Z
  • 1.9k
  • 11
  • 16

Stable vector bundle Projective or Injective?

I have a very easy question, which I couldn't get in the literature. Please forgive me if it is so easy!!! Question: Is a stable vector bundle over a curve $C$ is projective (as a $\mathcal O_C$-module) ? is it injective? Could you give me a reference?

Thanks