  I show how elliptic genera for various Calabi-Yau threefolds may be
understood from supergravity localization using the quantization of the phase
space of certain multi-center configurations. I present a simple procedure that
allows for the enumeration of all multi-center configurations contributing to
the polar sector of the elliptic genera\textemdash explicitly verifying this in
the cases of the quintic in $\mathbb{P}^4$, the sextic in
$\mathbb{WP}_{(2,1,1,1,1)}$, the octic in $\mathbb{WP}_{(4,1,1,1,1)}$ and the
dectic in $\mathbb{WP}_{(5,2,1,1,1)}$. With an input of the corresponding
`single-center' indices (Donaldson-Thomas invariants), the polar terms have
been known to determine the elliptic genera completely. I argue that this
multi-center approach to the low-lying spectrum of the elliptic genera is a
stepping stone towards an understanding of the exact microscopic states that
contribute to supersymmetric single center black hole entropy in
$\mathcal{N}=2$ supergravity.
