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Seiberg-Witten geometry of mass deformed $\mathcal N=2$ superconformal ADEquiver gauge theories in four dimensions is determined. We solve the limitshape equations derived from the gauge theory and identify the space $\mathfrakM$ of vacua of the theory with the moduli space of the genus zero holomorphic(quasi)maps to the moduli space ${\rm Bun}_{\mathbf G} (\mathcal E)$ ofholomorphic $G^{\mathbb C}$-bundles on a (possibly degenerate) elliptic curve$\mathcal E$ defined in terms of the microscopic gauge couplings, for thecorresponding simple ADE Lie group $G$. The integrable systems $\mathfrak P$underlying the special geometry of $\mathfrak M$ are identified. The modulispaces of framed $G$-instantons on ${\mathbb R}^{2} \times {\mathbb T}^{2}$, of$G$-monopoles with singularities on ${\mathbb R}^{2} \times {\mathbb S}^{1}$,the Hitchin systems on curves with punctures, as well as various spin chainsplay an important r\^ole in our story. We also comment on thehigher-dimensional theories.

Seiberg-Witten Geometry of Four-Dimensional $\mathcal N=2$ Quiver Gauge Theories