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Locally free sheaves

Algebraic Geometry
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PJPu17
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Locally free sheaves

#1

Post by PJPu17 » Sun Dec 17, 2017 12:58 am

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 \[\Lambda^{r}{\cal{E}}\cong\Lambda^{r'}{\cal{E}}'\otimes\Lambda^{r''}{\cal{E}}''\,.\]
Last edited by admin on Sun Dec 17, 2017 4:23 am, edited 1 time in total.
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Tsakanikas Nickos
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Re: Locally free sheaves

#2

Post by Tsakanikas Nickos » Tue Dec 19, 2017 12:40 am

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]
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