Positive Cones of Parabolic Grassmann Bundle over a curve

In this article, we define the parabolic Grassmann bundle associated to a parabolic vector bundle over a smooth projective variety, generalizing the construction of parabolic projective bundles developed in \cite{BL}.

We determine its Néron--Severi group and compute its nef, pseudoeffective, and Mori cones over smooth projective curves.

We also compute the corresponding cones for the fiber product of two parabolic Grassmann bundles over a smooth projective curve.