On Subvarieties of Degenerations of Fano Varieties
arXiv:2109.11958 · doi:10.1142/S0129167X24500575
Abstract
The goal of this work is to study geometric properties of geometrically irreducible subschemes on degenerations of Fano varieties (more generally, of separably rationally connected varieties). It is known that these geometrically irreducible subschemes exist when the ground field has characteristic zero or contains an algebraically closed subfield. We show that the dimension of this geometrically irreducible subscheme has a lower bound by the Fano index of the generic fibre.
arXiv commentFinal version, the article has been rewritten throughout according to the suggestions from the referees, accepted by Internat. J. Math