2026-09-23T07:21:14Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/101520 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

DSpace SAF Submission Ingestion Package generated from Vireo submission #12706 on 2018-09-27 at 10:46:21 Made available in DSpace on 2018-09-27T16:17:36Z (GMT). No. of bitstreams: 2 OCHOADEALAIZAGRACIA-DISSERTATION-2018.pdf: 572835 bytes, checksum: 2ec87f6e002f8524777409d7cb5d7dcf (MD5) LICENSE.txt: 4226 bytes, checksum: abfff410eef9312fe29beaf2e0ecd227 (MD5) Previous issue date: 2018-07-06 application/pdf http://hdl.handle.net/2142/101520 en Copyright 2018 by Itziar Ochoa de Alaiza Gracia. All rights reserved. Nevins, Thomas Loja Fernandes, Rui Yong, Alexander Dodd, Christopher Ochoa de Alaiza Gracia, Itziar 2018-09-27T16:17:36Z 2018-09-27T16:17:36Z 2018-07-06 2018-08 Given an algebraic variety $X$ with an action of a reductive group $G$, geometric invariant theory splits $X$ as the disjoint union $X=X^{ss}\sqcup X^{un}$ of the semistable and unstable locus. The Kirwan-Ness stratification refines $X$ even more by describing $X^{un}$ as a disjoint union of strata $X^{un}=\displaystyle\sqcup_{\beta\in\textsf{KN}} S_\beta$ detemined by 1-parameter subgroups $\beta$. In this thesis we study the 1-parameter subgroups that determine the Kirwan-Ness stratifications of representations. We will describe an algorithm that finds the $\beta$'s and we show that such algorithm can be simplified when our space is of the form $T^*V$ where $V$ is a vector space. We go on to investigate more deeply the 1-parameter subgroups in the case of the space of representations $\text{Rep}(Q,v)$ of a cyclic quiver $Q$. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-09-27 without embargo terms The student, Itziar Ochoa de Alaiza Gracia, accepted the attached license on 2018-07-02 at 15:46. The student, Itziar Ochoa de Alaiza Gracia, submitted this Dissertation for approval on 2018-07-02 at 15:47. This Dissertation was approved for publication on 2018-07-06 at 09:02. Representations, quivers. Stratifications of representations and cyclic quivers text text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.