A finiteness theorem for low-codimensional nonsingular subvarieties of quadrics
Abstract
We prove that there are only finitely many families of codimension two nonsingular subvarieties of quadrics $\Q{n}$ which are not of general type, for
n=5
and
n≥7
. We prove a similar statement also for the case of higher codimension. The case
n=6
has been recently settled by Fania-Ottaviani.
Keywords: Codimension two, Grassmannians, Lifting, Low codimension, Not of General Type, Polynomial Bound, Quadrics