Title: The Painlevé property of $\mathbb{C}P^{N-1}$ sigma models,
Abstract: We test the $\mathbb{C}P^{N-1}$ sigma models for the Painlevé property.
While the construction of finite action solutions ensures their meromorphicity,
the general case requires testing. The test is performed for the equations in
the homogeneous variables, with their first component normalised to one. No
constraints are imposed on the dimensionality of the model or the values of the
initial exponents. This makes the test nontrivial, as the number of equations
and dependent variables are indefinite. A $\mathbb{C}P^{N-1}$ system proves to
have a $(4N-5)$-parameter family of solutions whose movable singularities are
only poles, while the order of the investigated system is $4N-4$. The remaining
degree of freedom, connected with an extra negative resonance, may correspond
to a branching movable essential singularity. An example of such a solution is
provided.