Algebraic Curves: An Introduction to Algebraic Geometry (2008 free edition)
by William Fulton · Reed College (author-authorized free edition)
The canonical entry point to algebraic curves and the reference nearly every syllabus and MathOverflow reading-order answer names first. Fulton's 1969 text, revised 2008 and released free by the author. Builds affine and projective plane curves, local rings, intersection numbers, Bezout's theorem, divisors and Riemann-Roch in about 120 pages, with exercises throughout.
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Algebraic Curves
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