2016/10/13 by Lindner, Niels · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1610.04077
A projective hypersurface X ⊆ \mathbb Pn has defect if hi(X) ≠ hi(\mathbb Pn) for some i ∈ \n, …, 2n-2\ in a suitable cohomology theory. This occurs for example when X ⊆ \mathbb P4 is not \mathbb Q-factorial. We show that in characteristic 0, the Tjurina number of hypersurfaces with defect is large. For X with mild singularities, there is a similar result in positive characteristic. As an application, we obtain a lower bound on the asymptotic density of hypersurfaces without defect over a finite field.