By Robin Hartshorne
From the preface:
"This publication offers an creation to summary algebraic geometry utilizing the equipment of schemes and cohomology. the most gadgets of research are algebraic types in an affine or projective house over an algebraically closed box; those are brought in bankruptcy I, to set up a couple of uncomplicated ideas and examples. Then the equipment of schemes and cohomology are built in Chapters II and III, with emphasis on functions instead of over the top generality. The final chapters of the ebook (IV and V) use those easy methods to examine subject matters within the classical conception of algebraic curves and surfaces."
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Algebraic Geometry (Graduate Texts in Mathematics) by Robin Hartshorne