Geodesic
Threefolds of Order One in the Six-Quadric
Informatics and Automation, Multidimensional algebraic geometry, Tome 264 (2009), pp. 25-36 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $Q_6$. 
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L. Borisov; J. Viaclovsky. Threefolds of Order One in the Six-Quadric. Informatics and Automation, Multidimensional algebraic geometry, Tome 264 (2009), pp. 25-36. http://geodesic.mathdoc.fr/item/TRSPY_2009_264_a2/

[1] Borisov L., Salamon S., Viaclovsky J., Orthogonal complex structures in Euclidean spaces, Preprint, Univ. Wisconsin and Politechn. Torino, 2008 | MR | Zbl

[2] Cartan É., The theory of spinors, Dover Publ., New York, 1981 | MR | Zbl

[3] Fulton W., Intersection theory, 2nd ed., Ergebn. Math. und ihrer Grenzgeb. (3), 2, Springer, Berlin, 1998 | MR | Zbl

[4] Griffiths P., Harris J., Principles of algebraic geometry, J. Wiley Sons, New York, 1994 | MR

[5] Gross M., “The distribution of bidegrees of smooth surfaces in $\mathrm{Gr}(1,\mathbf P^3)$”, Math. Ann., 292:1 (1992), 127–147 | DOI | MR | Zbl

[6] Hartshorne R., Algebraic geometry, Grad. Texts Math., 52, Springer, New York, 1977 | DOI | MR | Zbl

[7] Ran Z., “Surfaces of order 1 in Grassmannians”, J. reine und angew. Math., 368 (1986), 119–126 | MR | Zbl

[8] Salamon S., Viaclovsky J., “Orthogonal complex structures on domains in $\mathbb R^4$”, Math. Ann. (to appear) | MR