Abstract:
Consider the smooth quadric $Q_6$ in $\mathbb P^7$. The middle homology group $H_6(Q_6,\mathbb Z)$ is isomorphic to $\mathbb Z\oplus\mathbb Z$, with a basis given by two classes of linear subspaces. We classify all threefolds of bidegree $(1,p)$ inside $Q_6$.
Citation:
L. Borisov, J. Viaclovsky, “Threefolds of Order One in the Six-Quadric”, Multidimensional algebraic geometry, Collected papers. Dedicated to the Memory of Vasilii Alekseevich Iskovskikh, Corresponding Member of the Russian Academy of Sciences, Trudy Mat. Inst. Steklova, 264, MAIK Nauka/Interperiodica, Moscow, 2009, 25–36; Proc. Steklov Inst. Math., 264 (2009), 18–29
\Bibitem{BorVia09}
\by L.~Borisov, J.~Viaclovsky
\paper Threefolds of Order One in the Six-Quadric
\inbook Multidimensional algebraic geometry
\bookinfo Collected papers. Dedicated to the Memory of Vasilii Alekseevich Iskovskikh, Corresponding Member of the Russian Academy of Sciences
\serial Trudy Mat. Inst. Steklova
\yr 2009
\vol 264
\pages 25--36
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2009
\vol 264
\pages 18--29
\crossref{https://doi.org/10.1134/S0081543809010039}
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