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You searched for subject:(quiver flag variety). Showing records 1 – 2 of 2 total matches.

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1. Green, James. Reconstructing certain quiver flag varieties from a tilting bundle.

Degree: PhD, 2018, University of Bath

Given a quiver flag variety Y equipped with a tilting bundle E, a construction ofCraw, Ito and Karmazyn [CIK18] produces a closed immersion fE : Y -> M(E), where M(E) is the fine moduli space of cyclic modules over the algebra End(E).In this thesis we present two classes of examples where fE is an isomorphism. Firstly, when Y is toric and E is the tilting bundle from [Cra11]; this generalises the well-known fact that Pn can be recovered from the endomorphism algebra of ⊕0 ≤  i  ≤  n OPn(i). Secondly, when Y = Gr(n, 2), the Grassmannian of 2-dimensional quotients of kn and E is the tilting bundle from [Kap84]. In each case, we give a presentation of the tilting algebra A = End(E) by constructing a quiver Q' such that there is a surjective k-algebra homomorphism Φ: kQ' -> A, and then give an explicit description of the kernel.

Subjects/Keywords: 510; quiver flag variety; tilting bundle

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Green, J. (2018). Reconstructing certain quiver flag varieties from a tilting bundle. (Doctoral Dissertation). University of Bath. Retrieved from https://researchportal.bath.ac.uk/en/studentthesis/reconstructing-certain-quiver-flag-varieties-from-a-tilting-bundle(c969e3db-f526-440e-a681-fffa5434a53c).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.767562

Chicago Manual of Style (16th Edition):

Green, James. “Reconstructing certain quiver flag varieties from a tilting bundle.” 2018. Doctoral Dissertation, University of Bath. Accessed September 29, 2020. https://researchportal.bath.ac.uk/en/studentthesis/reconstructing-certain-quiver-flag-varieties-from-a-tilting-bundle(c969e3db-f526-440e-a681-fffa5434a53c).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.767562.

MLA Handbook (7th Edition):

Green, James. “Reconstructing certain quiver flag varieties from a tilting bundle.” 2018. Web. 29 Sep 2020.

Vancouver:

Green J. Reconstructing certain quiver flag varieties from a tilting bundle. [Internet] [Doctoral dissertation]. University of Bath; 2018. [cited 2020 Sep 29]. Available from: https://researchportal.bath.ac.uk/en/studentthesis/reconstructing-certain-quiver-flag-varieties-from-a-tilting-bundle(c969e3db-f526-440e-a681-fffa5434a53c).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.767562.

Council of Science Editors:

Green J. Reconstructing certain quiver flag varieties from a tilting bundle. [Doctoral Dissertation]. University of Bath; 2018. Available from: https://researchportal.bath.ac.uk/en/studentthesis/reconstructing-certain-quiver-flag-varieties-from-a-tilting-bundle(c969e3db-f526-440e-a681-fffa5434a53c).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.767562

2. Im, Mee Seong. On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution.

Degree: PhD, 0439, 2014, University of Illinois – Urbana-Champaign

We introduce the notion of filtered representations of quivers, which is related to usual quiver representations, but is a systematic generalization of conjugacy classes of n ×  n matrices to (block) upper triangular matrices up to conjugation by invertible (block) upper triangular matrices. With this notion in mind, we describe the ring of invariant polynomials for interesting families of quivers, namely, finite ADE-Dynkin quivers and affine type \widetilde{A}-Dynkin quivers. We then study their relation to an important and fundamental object in representation theory called the Grothendieck-Springer resolution, and we conclude by stating several conjectures, suggesting further research. Advisors/Committee Members: Nevins, Thomas A. (advisor), Kedem, Rinat (Committee Chair), Nevins, Thomas A. (committee member), Bergvelt, Maarten J. (committee member), Schenck, Henry K. (committee member).

Subjects/Keywords: Algebraic geometry; representation theory; quiver varieties; filtered quiver variety; quiver flag variety; semi-invariant polynomials; invariant subring; Derksen-Weyman; Domokos-Zubkov; Schofield-van den Bergh; ADE-Dynkin quivers; affine Dynkin quivers; quivers with at most two pathways between any two vertices; filtration of vector spaces; classical invariant theory; the Hamiltonian reduction of the cotangent bundle of the enhanced Grothendieck-Springer resolution; almost-commuting varieties; affine quotient

…subset of quiver representations with a notion of a flag ([HM11] and [SW11… …x5D;), generalized Grothendieck-Springer resolutions whose fibers are quiver flag… …Jordan quiver. Equip Cn with the complete standard flag of vector spaces, {0} ⊂ C1… …Grassmannians and quiver flag varieties through objects called universal quiver Grassmannian (cf… …Section 3.1.1) and universal quiver flag (cf. Section 3.1.2). In Chapter 4, we… 

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Im, M. S. (2014). On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/49392

Chicago Manual of Style (16th Edition):

Im, Mee Seong. “On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution.” 2014. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed September 29, 2020. http://hdl.handle.net/2142/49392.

MLA Handbook (7th Edition):

Im, Mee Seong. “On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution.” 2014. Web. 29 Sep 2020.

Vancouver:

Im MS. On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2014. [cited 2020 Sep 29]. Available from: http://hdl.handle.net/2142/49392.

Council of Science Editors:

Im MS. On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2014. Available from: http://hdl.handle.net/2142/49392

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