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I would like to start ideas of localy ringed space, schemes, sheaf and their uses and properties and examples from very elementary level. would any one suggest me a book or notes which explains those things with lots of examples may be some pictures etc?

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up vote 1 down vote accepted

A book from which I learned a lot is Algebraic Geomtry - An Introduction by Daniel Perrin. Chapter 3 gives a nice motivation for sheaves and locally ringed spaces, without being too abstract. Also, I recommend The geometry of schemes by Joe Harris and David Eisenbud.

But you won't get everything from these books. For more advanced stuff, I recommend the (classic) Algebraic Geometry by Robin Hartshorne and the (not-so classic but very good) Algebraic geometry and arithmetic curves by Qing Liu.

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thank you dear sir :) – Un Chien Andalou May 21 '12 at 15:14
And by the way, the first two books I mentionned are available online through the library of my university; it may be the case that they are also available through yours – M Turgeon May 21 '12 at 15:18
it would be great, if you give the link of pdf of those? – Un Chien Andalou May 21 '12 at 15:20
@Makuasi You will have to look through your university's library. For example, if I search for The geometry of schemes, I get the following:… , and it tells me that there is an eletronic copy available. But this depends on what kind of subscriptions you university has, and the resources provided by the library. – M Turgeon May 21 '12 at 15:30
ok dear sir, i will collect it. :) – Un Chien Andalou May 21 '12 at 15:31

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