Locally free sheaves

Algebraic Geometry
Post Reply
PJPu17
Posts: 10
Joined: Mon Oct 17, 2016 9:33 pm

Locally free sheaves

#1

Post by PJPu17 »

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.
Reason: LaTeX
Tsakanikas Nickos
Community Team
Posts: 314
Joined: Tue Nov 10, 2015 8:25 pm

Re: Locally free sheaves

#2

Post by Tsakanikas Nickos »

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]
Post Reply

Create an account or sign in to join the discussion

You need to be a member in order to post a reply

Create an account

Not a member? register to join our community
Members can start their own topics & subscribe to topics
It’s free and only takes a minute

Register

Sign in

Who is online

Users browsing this forum: No registered users and 2 guests