On the behaviour of strong semistability in geometric deformations (Q405391)

``Recall that a vector bundle on a smooth projective curve over a field of positive characteristic is called strongly semistable if all its Frobenius pull-backs are semistable.'' In this paper, the authors give examples of vector bundles on a relative smooth curve \(Y \to B\), \(B\) affine, which are ``generically strongly semistable and semistable but not strongly semistable for some special fibre''. They use ``syzygy bundles'', i.e. kernels of surjective maps of the shape \((f_1,\dots f_n): \bigoplus _{i=1}^{n} {\mathcal O}_Y(-d_i) \to {\mathcal O}_Y\).