Algebraic Geometry: Some References

Curves

• Clemens, A scrapbook of complex curve theory, AMS.
• Coolidge, Treatise on algebraic plane curves, Dover.
• Forster, Lectures on Riemann surfaces, Springer.
• Fulton, Algebraic curves, Benjamin/Cummings
• Mumford, Curves and their Jacobians, Univ. of Michigan Press
• Narasimhan, Compact Riemann surfaces, Birkhauser.
• Walker, Algebraic curves, Princeton UP.

Varieties (before schemes)

• Dolgachev, Topics in classical algebraic geometry, lecture notes.
• Eisenbud, Geometry of syzygies.
• Griffiths and Harris, Principles of algebraic geometry, Wiley.
• Harris, Algebraic geometry: a first course, Springer.
• Hodge and Pedoe, Methods of algebraic geometry I & II, Cambridge UP.
• Kempf, Algebraic varieties, Cambridge UP. [On reserve in library]
• Mumford, Algebraic geometry I: complex projective varieties, Springer.
• Reid, Undergraduate algebraic geometry, Cambridge UP.
• Shafarevich, Basic algebraic geometry, volume I, Springer. [On reserve in library]

Schemes and their cohomology

• Bredon, Sheaf theory, McGraw-Hill and Springer.
• Eisenbud and Harris, Geometry of schemes, Springer. [On reserve in library]
• Eisenbud et al., Computations in algebraic geometry with Macaulay 2.
• Godement, Topologie algebrique et theorie des faisceaux, Hermann.
• Grothendieck, Elements de geometrie algebrique, Publ. Math. IHES: I,  II,  III.1,  III.2,  IV.1,  IV.2,  IV.3,  IV.4.
• Hartshorne, Algebraic geometry, Springer. [On reserve in library]
• Iversen, Cohomology of sheaves, Springer.
• D. Mumford, Red book of varieties and schemes, Springer.
• Serre, ``Faisceaux algebriques coherents'' (AKA ``FAC'').
• Shafarevich, Basic algebraic geometry, volume II, Springer. [On reserve in library]
• Swan, Theory of sheaves, U. Chicago Press.

Commutative algebra

• M. Atiyah and I. MacDonald, Introduction to commutative algebra, Addison-Wesley.
• D. Eisenbud, Commutative algebra with a view toward algebraic geometry, Springer, 1995.
• Matsumura, Commutative ring theory, Cambridge UP.
• Nagata, Local rings, Interscience.
• Northcott, Ideal theory, Cambridge UP.

Surfaces

• Barth, Peters, and Van de Ven, Compact complex surfaces, Springer.
• Beauville, Complex algebraic surfaces, Cambridge UP.
• Manin, Cubic forms, North-Holland.
• Segre, Nonsingular cubic surfaces, Oxford UP.
• Shafarevich et al., Algebraic surfaces, AMS 1967.

Topics in the geometry of curves

• Arbarello, Cornalba, Griffiths, and Harris, Geometry of algebraic curves, volume 1, Springer.
• Dijkgraaf, Faber, and van der Geer, eds., The moduli space of curves, Birkhauser.
• Harris, Curves in projective space, Presses de l'Universite de Montreal.
• Harris and Morrison, Moduli of curves, Springer.
• Lehavi, ``Any smooth plane quartic can be reconstructed from its bitangents,'' preprint.