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I am currently an undergraduate mathematics student who is interested in studying more about complex/analytic geometry. However, most undergraduate modules (at least in my home university) do not cover the substantial background material required to understand the myriad theorems and lemmas in that area of mathematics i.e. several complex variables, complex manifolds, algebraic geometry, sheaves....

Hence, what texts can I use as introductory material to build up the necessary foundation. A friend recommended Atiyah and Macdonald as a precursor to the algebra required for Hartshorne's Algebraic Geometry. Are there any other recommendations (i.e. texts that might cover the topics listed above)?

P.S. I have completed the usual undergraduate courses in complex analysis, algebra and analysis.

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  • $\begingroup$ When I was a student, I liked the book of Taylor "Several Complex Variables with Connections to Algebraic Geometry and Lie Groups". There is all the essential background in commutative algebra, homological algebra, complex analysis, as well as deep theorems such as GAGA, Hodge theorem... with their proof. $\endgroup$
    – Roland
    May 9, 2020 at 8:51

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I think the book Algebraic and Analytic Geometry by Neeman might be a good option. It is entirely focused on showing some connections between algebraic and analytic geometry, including GAGA.

I believe its target audience is around the end of an undergraduate programme, so shouldn't be intractable.

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  • $\begingroup$ I did a course with Amnon in my second year of undergraduate, working through his book. It is a very good read! $\endgroup$
    – AmorFati
    Aug 23, 2020 at 8:13

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