Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 069, 13 pages      arXiv:2003.05890      https://doi.org/10.3842/SIGMA.2020.069
Contribution to the Special Issue on Noncommutative Manifolds and their Symmetries in honour of Giovanni Landi

On the Irreducibility of Some Quiver Varieties

Claudio Bartocci ^ab, Ugo Bruzzo ^cdefg, Valeriano Lanza ^h and 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) SISSA (Scuola Internazionale Superiore di Studi Avanzati), Via Bonomea 265, 34136 Trieste, Italy
^d) Departamento de Matemática, Universidade Federal da Paraíba, Campus I, João Pessoa, PB, Brasil
^e) IGAP (Institute for Geometry and Physics), Trieste, Italy
^f) INFN (Istituto Nazionale di Fisica Nucleare), Sezione di 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

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

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 $n \ge 1$.

Key words: quiver representations; Hilbert schemes of points.

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