# Introduction to Plane Algebraic Curves

• Ernst Kunz
Textbook

1. Front Matter
Pages i-xii
2. ### Plane Algebraic Curves

1. Front Matter
Pages 1-1
2. Pages 3-12
3. Pages 13-21
4. Pages 31-37
5. Pages 61-72
6. Pages 81-87
7. Pages 89-97
8. Pages 99-115
9. Pages 117-130
10. Pages 131-142
11. Pages 149-160
12. Pages 161-173
13. Pages 175-185
3. Back Matter
Pages 187-293

### Introduction

This work treats an introduction to commutative ring theory and algebraic plane curves, requiring of the student only a basic knowledge of algebra, with all of the algebraic facts collected into several appendices that can be easily referred to, as needed.

Kunz's proven conception of teaching topics in commutative algebra together with their applications to algebraic geometry makes this book significantly different from others on plane algebraic curves. The exposition focuses on the purely algebraic aspects of plane curve theory, leaving the topological and analytical viewpoints in the background, with only casual references to these subjects and suggestions for further reading.

Most important to this text:

* Emphasizes and utilizes the theory of filtered algebras, their graduated rings and Rees algebras, to deduce basic facts about the intersection theory of plane curves

* Presents residue theory in the affine plane and its applications to intersection theory

* Methods of proof for the Riemann–Roch theorem conform to the presentation of curve theory, formulated in the language of filtrations and associated graded rings

* Examples, exercises, figures and suggestions for further study round out this fairly self-contained textbook

From a review of the German edition:

"[T]he reader is invited to learn some topics from commutative ring theory by mainly studying their illustrations and applications in plane curve theory. This methodical approach is certainly very enlightening and efficient for both teachers and students… The whole text is a real masterpiece of clarity, rigor, comprehension, methodical skill, algebraic and geometric motivation…highly enlightening, motivating and entertaining at the same time… One simply cannot do better in writing such a textbook."

—Zentralblatt MATH

### Keywords

Algebraic curve Belshoff Kunz algebra computer algebra ksa ring theory

#### Authors and affiliations

• Ernst Kunz
• 1
1. 1.NWF I - MathematikUniversitäat RegensburgRegensburgGermany