TY  - BOOK
AU  - Eisenbud,David
AU  - Harris,Joe
TI  - The practice of algebraic curves: a second course in algebraic geometry 
T2  - Graduate studies in mathematics
SN  - 9781470479435
U1  - 516.352 23
PY  - 2025///
CY  - Providence, Rhode Island
PB  - American Mathematical Society
KW  - Algebraic curves
KW  - Algebraic geometry
KW  - Projective geometry
KW  - Riemann-Roch theorem
KW  - Moduli theory
N1  - Includes bibliographical references and index; Plane algebraic curves -- Divisors and linear systems -- Projective varieties -- Morphisms and rational maps -- Riemann-Roch theorem -- Singularities and normalization -- Intersection theory -- Moduli of curves -- Brill-Noether theory -- Computational methods and examples
N2  - This advanced graduate-level textbook provides a comprehensive introduction to algebraic curves and modern algebraic geometry through a strongly example-driven and computational approach. Building upon foundational ideas in algebra, geometry, and topology, the book develops the theory of plane curves, divisors, linear systems, projective varieties, and morphisms while emphasizing geometric intuition and practical techniques. The authors systematically introduce core concepts such as singularities, normalization, intersection multiplicities, Riemann-Roch theory, moduli spaces, and Brill-Noether theory, illustrating how abstract algebraic methods can be applied to concrete geometric problems. Numerous worked examples, exercises, and computational perspectives help readers understand both the classical and modern aspects of algebraic geometry. Designed for graduate students and researchers, the work serves as a second course in algebraic geometry and an accessible bridge to advanced research literature in algebraic and arithmetic geometry
ER  -