Let $X_w$ be a Schubert subvariety of a cominuscule Grassmannian $X$. We construct a resolution of singularities for the conormal variety $T^*_XX_w$ of $X_w$. When $X$ is of type A,B,C,D, we use this to compute a system of defining equations for $T^*_XX_w$ as a subvariety of the cotangent bundle $T^*X$ set-theoretically. Finally, we show how this also yields a system of defining equations for certain orbital varieties.

Based on https://arxiv.org/abs/1805.12297