Hi I´m stuck with the following proposition, could you help me to solve it?
Suppose $0\rightarrow{\cal{E}}'\rightarrow{\cal{E}}\rightarrow{\cal{E}}''\rightarrow0$ is an exact sequence of locally free sheaves of ranks $r'\,, \, r$ and $r''$. Then \[\Lambda^{r}{\cal{E}}\cong\Lambda^{r'}{\cal{E}}'\otimes\Lambda^{r''}{\cal{E}}''\,.\]
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Locally free sheaves
Locally free sheaves
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Re: Locally free sheaves
Hi!
You can find an answer to your question in the following reference: [Q. Liu  Algebraic Geometry and Arithmetic Curves  Chapter 6 / Lemma 4.1 & Corollary 4.2]
You can find an answer to your question in the following reference: [Q. Liu  Algebraic Geometry and Arithmetic Curves  Chapter 6 / Lemma 4.1 & Corollary 4.2]