Density of quasismooth hypersurfaces in simplicial toric varieties

摘要

This paper investigates the density of hypersurfaces in a projective normalsimplicial toric variety over a finite field having a quasismooth intersectionwith a given quasismooth subscheme. The result generalizes the formula found byB. Poonen for smooth projective varieties. As an application, we furtheranalyze the density of hypersurfaces with bounds on their number ofsingularities and on the length of their singular schemes.