Some rational subvarieties of moduli spaces of stable vector bundles

Let X be a smooth complex irreducible projective variety of dimension $n\ge 2$ and $H$ be an ample line bundle on $X$. In this paper, we construct families of ${\mu }_H$-stable vector bundles on $X$ having fixed determinant and rank $r$, which are generated by $r+1$ global sections, parametrized by Grassmanian varieties. This gives into the corresponding moduli spaces special subvarieties birational to Grassmannian.