Generalization of Gurjar's hyperplane section theorem to arbitrary analytic varieties and AmAC classes

Abstract

This paper aims to generalize the hyperplane section Theorem of R.V. Gurjar to arbitrary (local) analytic varieties, even if the intersection with hyperplanes is not necessarily isolated.

In the case of formal varieties, we generalize the statement to work for different classes of hypersurfaces other than hyperplanes. We call the classes of functions (which are subsets of the formal power series ring) defining these classes of hypersurface algebraic $m$-adically closed (A$m$AC) classes.