%0 Journal Article
%T Moduli of sheaves, Fourier-Mukai transform, and partial desingularization
%A Kiryong Chung
%A Han-Bom Moon
%J Mathematics
%D 2014
%I arXiv
%X We study birational maps among 1) the moduli space of semistable torsion sheaves of Hilbert polynomial $4m+2$ on a smooth quadric surface, 2) the moduli space of semistable torsion sheaves of Hilbert polynomial $m^{2}+3m+2$ on $\mathbb{P}^{3}$, 3) Kontsevich's moduli space of genus zero stable maps of degree 2 to Grassmannian $Gr(2, 4)$. A regular birational morphism from 1) to 2) is described in terms of Fourier-Mukai transform. The map from 3) to 2) is Kirwan's partial desingularization. Also we investigate several geometric properties of 1) by using the variation of moduli spaces of stable pairs.
%U http://arxiv.org/abs/1410.8211v3