Points and Curves in Affine Space
Date of Graduation
Summer 2005
Degree
Master of Science in Mathematics
Department
Mathematics
Committee Chair
Kishor Shah
Abstract
In the first part of our thesis, we carefully study five versions of the Hilbert’s Null-stellensatz, along with their proofs, as given in David Eisenbud’s Commutative Algebra with a View Toward Algebraic Geometry. We fill in the details for all the proofs. In the second part of our thesis, we explore curves with the parameterization {(t̂m, t̂(m+1),…,t̂(m+k)) │ t ∈ }, were m and k are positive integers. Our Variety Extension Therom determines the defining ideals of these curves under certain conditions. Our Exponent Set Criteria gives sufficient conditions for a polynomial to be zero. This is useful in showing that certain remainders are zero when applying the Division Algorithm. We conjecture a Java program that calculates the reduced Groebner basis for the ideals of these curves.
Keywords
Nullstellensatz, Noether normalization, monomial curve, integral, localization, Groebner basis, affine variety, commutative algebra, algebraic geometry
Subject Categories
Mathematics
Copyright
© Daniel R. Kopsas
Recommended Citation
Kopsas, Daniel R., "Points and Curves in Affine Space" (2005). MSU Graduate Theses/Dissertations. 1617.
https://bearworks.missouristate.edu/theses/1617
Dissertation/Thesis
