Moduli spaces of framed sheaves and quiver varieties

JOURNAL OF GEOMETRY AND PHYSICS

卷:118

Article

Bartocci, Claudio¹  Lanza, Valeriano²  Rava, Claudio L. S.¹ 

[1] Univ Genoa, Dipartimento Matemat, Genoa, Italy

[2] Univ Estadual Campinas, Inst Matemat Estat & Comp Cient, Campinas, SP, Brazil

关键词: Framed sheaves;    Quiver varieties;    Hirzebruch surfaces;    Monads;    ADHM data;   

DOI  :  10.1016/j.geomphys.2016.10.011

来源: Elsevier

【 摘 要 】

In the first part of this paper we provide a survey of some fundamental results about moduli spaces of framed sheaves on smooth projective surfaces. In particular, we outline a result by Bruzzo and Markushevich, and discuss a few significant examples. The moduli spaces of framed sheaves on P-2, on multiple blowup of P-2 are described in terms of ADHM data and, when this characterization is available, as quiver varieties. The second part is devoted to a detailed study of framed sheaves on the Hirzebruch surface Sigma(n) in the case when the invariant expressing the necessary and sufficient condition for the nonemptiness of moduli spaces attains its minimum (what we call the minimal case). Our main result is that, under this assumption, the corresponding moduli space is isomorphic to a Grassmannian (when n = 1), or to the direct sum of n - 1 copies of the cotangent bundle of a Grassmannian (when n >= 2). Finally, by slightly generalizing a construction due to Nakajima, we prove that these moduli spaces admit a description as quiver varieties. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free