Max Noether's Fundamental Theorem

Author

Jacob Aaron Boswell

Date of Graduation

Summer 2008

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Richard Belshoff

Abstract

In this paper, we introduce and give proofs of some basic concepts of algebraic geometry leading up to a proof of Max Noether's Fundamental Theorem. This theorem states that under certain conditions, a curve H passing through the common intersections of two other curves F and G will be equal to a combination AF + BG of the two. For this reason, it is sometimes referred to as "the AF + BG theorem." Examples using Noether's Theorem are given, including several from Fulton's Algebraic Curves.

Keywords

Algebra, algebraic curve, algebraic geometry, Noether's theorem, polynomial

Subject Categories

Mathematics

Copyright

© Jacob Aaron Boswell

Recommended Citation

Boswell, Jacob Aaron, "Max Noether's Fundamental Theorem" (2008). MSU Graduate Theses/Dissertations. 1628.
https://bearworks.missouristate.edu/theses/1628