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.
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