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Algebraic and complex geometry (book list)

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The subject description:

 4. Algebraic and complex geometry  
    Algebraic varieties, their cycles, cohomologies and motives (including positive characteristics). Schemes. 
    Commutative algebra. Low dimensional varieties. Singularities and classification. Birational geometry. 
    Moduli spaces. Abelian varieties and p-divisible groups. Derived categories. Transcendental methods, 
    topology of algebraic varieties. Complex differential geometry, Kahler manifolds and Hodge theory. 
    Relations with mathematical physics and representation theory. Real algebraic and analytic sets. Rigid and 
    p-adic analytic spaces. Tropical geometry.
    Connections with sections 2, 3, 5, 6, 7, 8, 14, 15.


Cartan, Henri; Eilenberg, Samuel Homological algebra. (English. English summary) With an appendix by David A. Buchsbaum. Reprint of the 1956 original. Princeton Landmarks in Mathematics. Princeton University Press, Princeton, NJ, 1999. xvi+390 pp. \$19.95. ISBN 0-691-04991-2


Algebraic Geometry

+* Brieskorn, Egbert and Knorrer, Horst. Plane Algebraic Curves New York, NY: Birkhauser, 1986.

Bruce, J.W. and Giblin, P.J. Curves and Singularities: A Geometrical Introduction to Singularity Theory New York, NY: Cambridge University Press, 1984.

Clemens, C. Herbert. A Scrapbook of Complex Curve Theory New York, NY: Plenum Press, 1980.

++Fulton, William. Algebraic Curves: An Introduction to Algebraic Geometry Reading, MA: W.A. Benjamin, 1969.

+Griffiths, Phillip A. Introduction to Algebraic Curves Providence, RI: American Mathematical Society, 1989.

++Griffiths, Phillip A. and Harris, Joseph. Principles of Algebraic Geometry New York, NY: John Wiley, 1978.

+* Kendig, Keith. Elementary Algebraic Geometry New York, NY: Springer-Verlag, 1987.

Orzech, Grace and Orzech, Morris. Plane Algebraic Curves: An Introduction Via Valuations New York, NY: Marcel Dekker, 1981.

+* Reid, Miles. Undergraduate Algebraic Geometry New York, NY: Cambridge University Press, 1988.

+* Seidenberg, A. Elements of the Theory of Algebraic Curves Reading, MA: Addison-Wesley, 1968.

+Seidenberg, A., ed. Studies in Algebraic Geometry Washington, DC: Mathematical Association of America, 1980.

+Semple, J.G. and Kneebone, G.T. Algebraic Curves New York, NY: Oxford University Press, 1959.

+* Semple, J.G. and Roth, L., eds. Introduction to Algebraic Geometry New York, NY: Oxford University Press, 1985.

++** Shafarevich, Igor R. Basic Algebraic Geometry New York, NY: Springer-Verlag, 1974.

+Walker, Robert J. Algebraic Curves New York, NY: Springer-Verlag, 1978.


Commutative Algebra

+** Atiyah, Michael F. and MacDonald, I.G. Introduction to Commutative Algebra Reading, MA: Addison-Wesley, 1969.

+* Bourbaki, Nicolas. Elements of Mathematics: Commutative Algebra, New York, NY: Springer-Verlag, 1989.

Hutchins, Harry C. Examples of Commutative Rings Washington, NJ: Polygonal, 1981.

+* Kaplansky, Irving. Commutative Rings, Boston, MA: Allyn and Bacon, 1974. Revised Edition.

+Kunz, E. Introduction to Commutative Algebra and Algebraic Geometry New York, NY: Birkhauser, 1985.

+Matsumura, Hideyuki. Commutative Ring Theory New York, NY: Cambridge University Press, 1986.

+* Nagata, Masayoshi. Local Rings New York, NY: Interscience, 1962.

+*** Zariski, Oscar and Samuel, Pierre. Commutative Algebra, New York, NY: Springer-Verlag, 1975, 1976. 2 Vols.

Homological Algebra

Geramita, Anthony V. and Small, Charles. Introduction to Homological Methods in Commutative Rings Kingston: Queen's University Press, 1976.

  • Hilton, Peter J. and Stammbach, U. A Course in Homological Algebra New York, NY: Springer-Verlag, 1971.
    • Mac Lane, Saunders. Homology New York, NY: Springer-Verlag, 1963.

Northcott, D.G. A First Course of Homological Algebra New York, NY: Cambridge University Press, 1973, 1980.

    • Rotman, Joseph J. An Introduction to Homological Algebra New York, NY: Academic Press, 1979.

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