Singular rationally connected surfaces with non-zero pluri-forms

This paper is concerned with projective rationally connected surfaces $X$ with canonical singularities and having non-zero pluri-forms, i.e. $({\mathrm{\Omega }}_X^1{)}^{[\otimes m]}$ has non-zero global sections for some m > 0, where $({\mathrm{\Omega }}_X^1{)}^{[\otimes m]}$ is the reflexive hull of $(\Omega_X^1)^{\otimes m}$. We show that any such surface can be obtained from a rational ruled surface by a very explicit sequence of blow-ups and blow-downs. Moreover, we interpret the existence of non-zero pluri-forms in terms of semistable reduction.