TY - JOUR A1 - Lindner, Niels T1 - Hypersurfaces with defect T2 - Journal of Algebra N2 - A projective hypersurface X⊆P^n has defect if h^i(X) ≠ h^i(P^n) for some i∈{n,…,2n−2} in a suitable cohomology theory. This occurs for example when X⊆P^4 is not Q-factorial. We show that hypersurfaces with defect tend to be very singular: In characteristic 0, we present a lower bound on the Tjurina number, where X is allowed to have arbitrary isolated singularities. For X with mild singularities, we prove a similar result in positive characteristic. As an application, we obtain an estimate on the asymptotic density of hypersurfaces without defect over a finite field. Y1 - 2020 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/8084 VL - 555 SP - 1 EP - 35 ER -