Mihai Pavel
Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania

We present several restriction theorems for semistable sheaves over a projective variety. Our results generalize the classical restriction theorems of Mehta and Ramanathan to the singular case, and they apply in particular to Gieseker-semistable sheaves. As an application, we construct different compactifications of the moduli space of vector bundles in higher dimensions.