Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Algebra
Q-Polymatroids And Their Application To Rank-Metric Codes., Benjamin Jany
Q-Polymatroids And Their Application To Rank-Metric Codes., Benjamin Jany
Theses and Dissertations--Mathematics
Matroid theory was first introduced to generalize the notion of linear independence. Since its introduction, the theory has found many applications in various areas of mathematics including coding theory. In recent years, q-matroids, the q-analogue of matroids, were reintroduced and found to be closely related to the theory of linear vector rank metric codes. This relation was then generalized to q-polymatroids and linear matrix rank metric codes. This dissertation aims at developing the theory of q-(poly)matroid and its relation to the theory of rank metric codes. In a first part, we recall and establish preliminary results for both q-polymatroids and …
Toric Bundles As Mori Dream Spaces, Courtney George
Toric Bundles As Mori Dream Spaces, Courtney George
Theses and Dissertations--Mathematics
A projective, normal variety is called a Mori dream space when its Cox ring is finitely generated. These spaces are desirable to have, as they behave nicely under the Minimal Model Program, but no complete classification of them yet exists. Some early work identified that all toric varieties are examples of Mori dream spaces, as their Cox rings are polynomial rings. Therefore, a natural next step is to investigate projectivized toric vector bundles. These spaces still carry much of the combinatorial data as toric varieties, but have more variable behavior that means that they aren't as straightforward as Mori dream …