Phillip A. Griffiths
Introduction to algebraic curves - Rhode Island: American Mathematical Society, [c1989] - 221 p - Translations of Mathematical Monographs Vol. 76 .
1. Fundamental concepts
2. The normalization theorem and its applications
3. The Riemann-Roch theorem
4. Applications of the Riemann-Roch theorem
5. Abel’s theorem and its applications
This book is based on a six-week series of lectures presented by the author to third- and fourth-year undergraduates and graduate students at Beijing University in 1982. The lectures began with minimal technical requirements (a working knowledge of elementary complex function theory and algebra together with some exposure to topology of compact surfaces) and proceeded directly to the Riemann-Roch and Abel theorems. This book differs from a number of recent books on this subject in that it combines analytic and geometric methods at the outset, so that the reader can grasp the basic results of the subject. Although such modern techniques of sheaf theory, cohomology, and commutative algebra are not covered here, the book provides a solid foundation to proceed to more advanced texts in general algebraic geometry, complex manifolds, and Riemann surfaces, as well as algebraic curves. Containing numerous exercises and two exams, this book would make an excellent introductory text. --- summary provided by publisher
9780821845370
Mathematics
QA565
Introduction to algebraic curves - Rhode Island: American Mathematical Society, [c1989] - 221 p - Translations of Mathematical Monographs Vol. 76 .
1. Fundamental concepts
2. The normalization theorem and its applications
3. The Riemann-Roch theorem
4. Applications of the Riemann-Roch theorem
5. Abel’s theorem and its applications
This book is based on a six-week series of lectures presented by the author to third- and fourth-year undergraduates and graduate students at Beijing University in 1982. The lectures began with minimal technical requirements (a working knowledge of elementary complex function theory and algebra together with some exposure to topology of compact surfaces) and proceeded directly to the Riemann-Roch and Abel theorems. This book differs from a number of recent books on this subject in that it combines analytic and geometric methods at the outset, so that the reader can grasp the basic results of the subject. Although such modern techniques of sheaf theory, cohomology, and commutative algebra are not covered here, the book provides a solid foundation to proceed to more advanced texts in general algebraic geometry, complex manifolds, and Riemann surfaces, as well as algebraic curves. Containing numerous exercises and two exams, this book would make an excellent introductory text. --- summary provided by publisher
9780821845370
Mathematics
QA565