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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 069, 13 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.069 (Mi sigma1606) 		 
On the Irreducibility of Some Quiver Varieties

Claudio Bartocciab, Ugo Bruzzocdefg, Valeriano Lanzah, Claudio L. S. Ravaa

a Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy
b Laboratoire SPHERE, CNRS, Université Paris Diderot (Paris 7), 75013 Paris, France
c INFN (Istituto Nazionale di Fisica Nucleare), Sezione di Trieste, Italy
d SISSA (Scuola Internazionale Superiore di Studi Avanzati), Via Bonomea 265, 34136 Trieste, Italy
e Departamento de Matemática, Universidade Federal da Paraíba, Campus I, João Pessoa, PB, Brasil
f IGAP (Institute for Geometry and Physics), Trieste, Italy
g Arnold-Regge Center for Algebra, Geometry and Theoretical Physics, Torino, Italy
h Departamento de Análise, IME, Universidade Federal Fluminense, Rua Professor Marcos Waldemar de Freitas Reis, Niterói, RJ, Brazil
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DOI: https://doi.org/10.3842/SIGMA.2020.069
Abstract: We prove that certain quiver varieties are irreducible and therefore are isomorphic to Hilbert schemes of points of the total spaces of the bundles $\mathcal O_{\mathbb P^1}(-n)$ for $n \ge 1$.
Keywords: quiver representations, Hilbert schemes of points.
Funding agency Grant number
INdAM-GNSAGA
PRIN
Fundação de Amparo à Pesquisa do Estado de São Paulo 2015/07766-4
2017/22052-9
This research was partly supported by INdAM-GNSAGA and PRIN “Geometria delle varietà algebriche”. V.L. was supported by the FAPESP Postdoctoral Grants No. 2015/07766-4 (Bolsa no País) and 2017/22052-9 (Bolsa Estágio de Pesquisa no Exterior).
Received: March 13, 2020; in final form July 10, 2020; Published online July 26, 2020
Bibliographic databases:
Document Type: Article
MSC: 14D20, 14D21, 14J60, 16G20
Language: English
Citation: Claudio Bartocci, Ugo Bruzzo, Valeriano Lanza, Claudio L. S. Rava, “On the Irreducibility of Some Quiver Varieties”, SIGMA, 16 (2020), 069, 13 pp.
Citation in format AMSBIB
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\by Claudio~Bartocci, Ugo~Bruzzo, Valeriano~Lanza, Claudio~L.~S.~Rava
\paper On the Irreducibility of Some Quiver Varieties
\jour SIGMA
\yr 2020
\vol 16
\papernumber 069
\totalpages 13
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\crossref{https://doi.org/10.3842/SIGMA.2020.069}
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