Grassmannians, Groebner Bases and Toric Ideals

✍ Scribed by Francesca Gandini

• Year: 2014
• Tongue: English
• Leaves: 64
• Series: Year 5 MMath Dissertation at University of Edinburgh
• Edition: version 7 Dec 2014
• Category: Library

✦ Table of Contents

Abstract......Page 2
Grassmaniannians......Page 4
G(2,4)......Page 5
Groebner Bases......Page 9
Lattice Polytopes......Page 15
A toric ideal......Page 21
Plücker coordinates......Page 24
Bracket ring......Page 29
Quadratic relations......Page 33
Grassmannians as varieties......Page 40
The action of the general linear group......Page 45
The ring bracket ring revisited......Page 46
Straightening sygyzies and the First Fundamental Theorem......Page 49
Initial algebras......Page 55
The maximal minors......Page 57
Toric degenerations......Page 59
Final remarks......Page 62