On the freeness of hypersurface arrangements consisting of hyperplanes and spheres

Abstract

Let V be a smooth variety. A hypersurface arrangement 𝓜 in V is a union of smooth hypersurfaces, which locally looks like a union of hyperplanes. We say 𝓜 is free if all these local models can be chosen to be free hyperplane arrangements. In this paper, we use Saito’s criterion to study the freeness of hypersurface arrangements consisting of hyperplanes and spheres, and construct the bases for the derivation modules explicitly.

Keywords

• hypersurface arrangement
• freeness
• hyperplane
• sphere
• 52c35
• 32s22