Claudio Bartocci, Ugo Bruzzo, Valeriano Lanza, Claudio L. S. Rava, “On the Irreducibility of Some Quiver Varieties”, SIGMA, 2020, Volume 16,069, 13 pp.

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SIGMA, 2020 Volume 16, 069, 13 pp. (Mi sigma1606)

On the Irreducibility of Some Quiver Varieties

Claudio Bartocci^ab, Ugo Bruzzo^cdefg, Valeriano Lanza^h, Claudio L. S. Rava^a

^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

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.

MSC: 14D20, 14D21, 14J60, 16G20

Received: March 13, 2020; in final form July 10, 2020; Published online July 26, 2020

Language: English

DOI: 10.3842/SIGMA.2020.069

Bibliographic databases:

ArXiv: 2003.05890

© Steklov Math. Inst. of RAS, 2024