Math 137: Algebraic Geometry, Spring 2014.
P. Griffiths and J. Harris Principles of Algebraic Geometry, Wiley-Interscience, 1978 (only Chapters 0, 1) Another useful references is D. Huybrechts Complex Geometry: an Introduction, Springer, 2004.
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of.
Turn in your homework solutions by sending electronic versions to me. Send your .tex file (I may comment on your LaTeX usage) and include your .pdf file as verification that your system produces the same thing as mine does.. Algebraic Geometry, a first course: Harris: Springer, 1995: Comparable: Algebraic Geometry: Hartshorne: Springer, 1977.
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Harshorne, Algebraic geometry. Eisenbud and Harris, Schemes. Gri ths and Harris, Principles of Algebraic Geometry. (This is complex alg.geom.) Matsumura, Commutative ring theory. Eisenbud, Commutative Algebra with a view toward Algebraic Geometry. Vakil, Foundations of algebraic geometry. (Online notes) RELATED COURSES.
David Eisenbud and Joe Harris: The Geometry of Schemes, GTM 197, Springer. A good introduction to schemes and related notions. Robin Hartshorne: Algebraic Geometry, Springer Verlag GTM 52, Springer. Still the most widely used introduction to modern algebraic geometry.
Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics.Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers.Modern definitions generalize this concept in several different ways, while attempting to preserve the geometric intuition behind the original definition.