A note about connectedness theorems a la Barth

Abstract

We prove Barth-type connectedness results for low-codimension smooth subvarieties with good numerical properties inside certain "easy" ambient spaces (such as homogeneous varieties, or spherical varieties). The argument employs some basics from the theory of cones of cycle classes, in particular the notion of bigness of a cycle class.

To appear (in slightly different form) in Geom. Dedicata. 11 pages, comments very welcome !

References in corpus (2)

• Small codimension smooth subvarieties in even-dimensional homogeneous spaces with Picard group $\mathbb{Z}$
• Small codimension subvarieties in homogeneous spaces