We introduce and study a surface defect in four dimensional gauge theories
supporting nested instantons with respect to the parabolic reduction of the
gauge group at the defect. This is engineered from a D3/D7-branes system on a
non compact Calabi-Yau threefold $X$. For $X=T^2 imes T^*{mathcal C}_{g,k}$,
the product of a two torus $T^2$ times the cotangent bundle over a Riemann
surface ${mathcal C}_{g,k}$ with marked points, we propose an effective theory
in the limit of small volume of ${mathcal C}_{g,k}$ given as a comet shaped
quiver gauge theory on $T^2$, the tail of the comet being made of a flag quiver
for each marked point and the head describing the degrees of freedom due to the
genus $g$. Mathematically, we obtain for a single D7-brane conjectural explicit
formulae for the virtual equivariant elliptic genus of a certain bundle over
the moduli space of the nested Hilbert scheme of points on the affine plane. A
connection with elliptic cohomology of character varieties and an elliptic
version of modified Macdonald polynomials naturally arises.
