Holmstrom Algebraic geometry

FGA EGA SGA english index

Add good introductory references. Should include:

Vakil: New revised book/course notes, see his blog.

http://mathoverflow.net/questions/28496/what-should-be-learned-in-a-first-serious-schemes-course

http://mathoverflow.net/questions/1291/a-learning-roadmap-for-algebraic-geometry

http://mathoverflow.net/questions/34110/algebraic-geometry-examples

http://mathoverflow.net/questions/78696/is-there-an-intuitive-reason-for-zariskis-main-theorem

http://mathoverflow.net/questions/111685/on-some-finiteness-properties-for-schemes

Mumford’s Red Book

Cox, Little, O'Shea: Ideals, varieties and algorithms

Dieudonne: History of AG

Putinar and Sullivant ed: Emerging applications of algebraic geometry

FGA, in folder AG/Various. Grothendieck topologies and stacks, Hilbert and Quot schemes, elementary deformation theory, Grothendieck’s existence thm in formal geometry, the Picard scheme, summary of intersection theory.

Totaro recommends Lazarsfeld: Positivity

Many useful insights are listed here: http://mathoverflow.net/questions/28496/what-should-be-learned-in-a-first-serious-schemes-course

http://mathoverflow.net/questions/46/what-is-the-universal-property-of-normalization

Bourbaki seminars possibly of some interest:

• Exp 37: Quelques varietes usuelles en G.A.
• exp 49: Hyperplane sections of normal varieties
• Exp 53: Picard vareity and Neron-Severi group
• Exp 71: Serre: Cohomology and complex variables
• Exp 72: Weil on Picard varieties and jacobians
• Exp 75: Equivalence relations on algebraic curves having multiple points
• Exp 66: Neron on arithmetic
• Exp 77: Serre: Cohomology and arithmetic
• Exp 78: Thom on subvarieties and homologu classes of differentiable varieties
• Possibly 84 and 85
• Exp 86: Samuel: Les fonctions holomorphes abstraites de Zariski
• Exp 88: Travaux de Hirzebruch sur la topologie des varietes
• Exp 89: Thom
• Exp 94: The Enriques-Severi Lemma
• Exp 95: Analytic sheaves
• Exp 99: Travaux de Zariski sur Hilbert 14.

---

Books in the folder AG/Introductory (only the most interesting listed)

• Abhyankar: AG for scientists and engineers. Very down-to-earth, actually quite nice! Goes up to RoS for surfaces and similar things.
• AG1 by Shokurov and Danilov: Basic theory of curves and Jacobians. Basic theory of varieties, some schemes at the end.
• Dieudonne: Algebraic Geometry. Notes in English surveying EGA I-III. (Course notes from Maryland)
• Dieudonne: Fondements de la GA Moderne. Continuation of the Maryland notes. Together these two sets of notes seem like a marvellous route into EGA.
• Dolgachev Topics in Classical AG: Polarity, Conics, Plane cubics, Determinental equations, Theta characteristics, Plane quartics, Planar Cremona transformations, Del Pezza surfaces, Cubic surfaces, Automorphisms of Del Pezzo surfaces, Geometry of Lines.
• Eisenbud-Harris: The geometry of schemes. Excellent book.
• Griffiths-Harris
• Harder: Lectures on AG (Vol 1 out of 3 planned): Basic homological algebra, sheaf theory, cohomology of sheaves, Riemanns surfaces and AVs
• Harris: First course. Classical, no schemes, many examples.
• Hartshorne
• Liu
• Parshin-Shafarevich AG III. Covers Hodge theory, periods, curves and Jacobians.
• Ravi Vakil book project
• Shafarevich ed AG II. Covers cohomology and algebraic surfaces.
• There is one big file with all the Russian AG books (I-V), ed Shafarevich
• Thomas Zeta functions. Contains basic function field arithmetic and some stuff on Weil conjectures.

nLab page on Algebraic geometry