BibTex format
@unpublished{Bellamy:2021,
author = {Bellamy, G and Schedler, T},
title = {Symplectic resolutions of quiver varieties and character varieties},
url = {http://hdl.handle.net/10044/1/70663},
year = {2021}
}
Publications
Citation
RIS format (EndNote, RefMan)
TY - UNPB
AB - In this article, we consider Nakajima quiver varieties from the point of view of symplectic algebraic geometry. We prove that they are all symplectic singularities in the sense of Beauville and completely classify which admit symplectic resolutions. Moreover we show that the smooth locus coincides with the locus of canonically $\theta$-polystable points, generalizing a result of Le Bruyn; we study their \'etale local structure, find their symplectic leaves, and we describe the Namikawa Weyl group. An interesting consequence of our results is that not all symplectic resolutions of quiver varieties appear to come from variation of GIT. We apply this to the $G$-character variety of a compact Riemann surface of genus $g > 0$, when $G$ is $\mathrm{SL}(n,\mathbb{C})$ or $\mathrm{GL}(n,\mathbb{C})$. We show that these varieties are symplectic singularities and classify when they admit symplectic resolutions: they do when $g = 1$ or $(g,n)=(2,2)$ (assuming $n \geq 2$). This is analogous to the case of a quiver with one vertex, $g$ arrows, and dimension vector $(n)$.
AU - Bellamy,G
AU - Schedler,T
PY - 2021///
TI - Symplectic resolutions of quiver varieties and character varieties
UR - http://hdl.handle.net/10044/1/70663
ER -