  Let $\mathbf{M}_d$ be the moduli space of stable sheaves on $\mathbb{P}^2$
with Hilbert polynomial $dm+1$. In this paper, we determine the effective and
the nef cone of the space $\mathbf{M}_d$ by natural geometric divisors. Main
idea is to use the wall-crossing on the space of Bridgeland stability
conditions and to compute the intersection numbers of divisors with curves by
using the Grothendieck-Riemann-Roch theorem. We also present the stable base
locus decomposition of the space $\mathbf{M}_6$. As a byproduct, we obtain the
Betti numbers of the moduli spaces, which confirm the prediction in physics.
