Eisenbud D. The Geometry of Syzygies. A Second Course in Commutative Algebra and Algebraic Geometry

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Springer, 2005. — 252 p. — ISBN: 0-387-22215-4.

First textbook-level account of basic examples and techniques in this area.
Suitable for self-study by a reader who knows a little commutative algebra and algebraic geometry already.