Abstract:In the early 80’s, V. Mehta and A. Ramanathan proved two restriction theorems which proved to be of central importance to the study of vector bundles in the subsequent years. The theorems roughly state that if X is a smooth projective variety over a field k = k with a polarisation H and V is a vector bundle on it which is semistable (resp. stable) w.r.t. H, then the restriction of V to a general, complete intersection curve of sufficiently high degree is again semistable (resp stable).
I will explain these theorems in detail and sketch a proof in some special cases. If time permits some applications will also be discussed.