Computational Algebraic Geometry Applied to Invariant Theory

Commutative algebra finds its roots in invariant theory and the connection is drawn from a modern standpoint. The Hilbert Basis Theorem and the Nullstellenstatz were considered lemmas for classical invariant theory. The Groebner basis is a modern tool used and is implemented with the computer algebra system Mathematica. Number 14 of Hilbert\'s 23 problems is discussed along with the notion of invariance under a group action of GLn(C). Computational difficulties are also discussed in reference to Groebner bases and Invariant theory.The straitening law is presented from a Groebner basis point of view and is motivated as being a key piece of machinery in proving First Fundamental Theorem of Invariant Theory.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2013

Author dc:creator

• Shifler, Ryan M.

Chair dc:contributor.committeechair

• Brown, Ezra A.

Committee members dc:contributor.committeemember

• Green, Edward L.
• Ball, Joseph A.

• Groebner Basis
• Invariant Theory
• Algorithm

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:810

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/23154