A finiteness theorem for low-codimensional nonsingular subvarieties of quadrics

Details A finiteness theorem for low-codimensional nonsingular subvarieties of quadrics A finiteness theorem for low-codimensional nonsingular subvarieties of quadrics

1996-08-21

arxiv.org/abs/alg-geom/9608020v1

Mathematics

Algebraic Geometry

Ams-LAtex;13 pages; to appear in Trans. A.M.S

Scientific paper

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 $n\geq 7$. 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

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