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Deep Points of Cluster Varieties /

Beyer, James Edward,

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Deep Points of Cluster Varieties /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Deep Points of Cluster Varieties // James Edward Beyer.
Author:	Beyer, James Edward,
Description:	1 electronic resource (192 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-11, Section: B.
Contained By:	Dissertations Abstracts International86-11B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31999278
ISBN:	9798314850473

Deep Points of Cluster Varieties /
Beyer, James Edward,

Deep Points of Cluster Varieties /James Edward Beyer. - 1 electronic resource (192 pages)

Source: Dissertations Abstracts International, Volume: 86-11, Section: B.

A cluster algebra determines an associated cluster variety, and each cluster determines a cluster torus in that variety. The cluster tori sometimes cover the entire cluster variety, but not always; we refer to any points not contained in any cluster torus as deep points. Any geometrically interesting points in the variety (e.g. singularities) must be deep, and many pathologies of the cluster algebra can be localized to those deep points.We describe the deep points of cluster algebras of unpunctured polygons, un-punctured marked surfaces, punctured polygons, and punctured surfaces with at least two boundary marked points. As a consequence, we classify the deep points of cluster algebras of types An and Dn. We also classify the deep points of the Markov cluster algebra -the cluster algebra of the once-punctured torus -and its upper cluster algebra. We then examine the deep points of skew-symmetrizable cluster algebras that arise from a folding of an acyclic quiver by a finite group of automorphisms. In particular, we study the deep points of cluster algebras of types Bn, Cn, and F4 via foldings of quivers of types A2n−1, Dn+1 and E6, respectively.

English

ISBN: 9798314850473Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Cluster algebras

Deep Points of Cluster Varieties /
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100 1 $a Beyer, James Edward, $e author. $0 (orcid)0000-0002-2499-2863 $3 3823109
245 1 0 $a Deep Points of Cluster Varieties / $c James Edward Beyer.
264 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2025
300 $a 1 electronic resource (192 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertations Abstracts International, Volume: 86-11, Section: B.
500 $a Advisors: Muller, Gregory Committee members: Mandel, Travis; Forester, Max; Livingood, Patrick.
502 $b Ph.D. $c University of Oklahoma - Graduate College $d 2025.
520 $a A cluster algebra determines an associated cluster variety, and each cluster determines a cluster torus in that variety. The cluster tori sometimes cover the entire cluster variety, but not always; we refer to any points not contained in any cluster torus as deep points. Any geometrically interesting points in the variety (e.g. singularities) must be deep, and many pathologies of the cluster algebra can be localized to those deep points.We describe the deep points of cluster algebras of unpunctured polygons, un-punctured marked surfaces, punctured polygons, and punctured surfaces with at least two boundary marked points. As a consequence, we classify the deep points of cluster algebras of types An and Dn. We also classify the deep points of the Markov cluster algebra -the cluster algebra of the once-punctured torus -and its upper cluster algebra. We then examine the deep points of skew-symmetrizable cluster algebras that arise from a folding of an acyclic quiver by a finite group of automorphisms. In particular, we study the deep points of cluster algebras of types Bn, Cn, and F4 via foldings of quivers of types A2n−1, Dn+1 and E6, respectively.
546 $a English
590 $a School code: 2409
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Applied mathematics. $3 2122814
650 4 $a Theoretical physics. $3 2144760
653 $a Cluster algebras
653 $a Cluster varieties
653 $a Deep points
653 $a Singularities
653 $a Skein algebras
653 $a Special points in varieties
690 $a 0405
690 $a 0642
690 $a 0753
690 $a 0364
710 2 $a University of Oklahoma - Graduate College. $b Mathematics: Arts & Sciences. $e degree granting institution. $3 3823110
720 1 $a Muller, Gregory $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-11B.
790 $a 2409
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31999278