Geodesic
On Fano varieties of genus 6
Izvestiya. Mathematics , Tome 21 (1983) no. 3, pp. 445-459

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In this paper it is proved that any nonsingular Fano variety $V_{10}$ of genus $6$ in $\mathbf P^7$ with $\operatorname{Pic}V_{10}\simeq\mathbf ZK_V$ is either a section $V_{10}^3$ of the Grassmannian $G(1,4)$ of lines in $\mathbf P^4$ by two hyperplanes and a quadric under the Plücker embedding of $G(1,4)$ in $\mathbf P^9$ or is the intersection ${V_{10}^3}'$ of a quadric and a cone over a section of $G(1,4)$ by a subspace of codimension $3$. Bibliography: 13 titles. 
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     author = {N. P. Gushel'},
     title = {On {Fano} varieties of genus 6},
     journal = {Izvestiya. Mathematics },
     pages = {445--459},
     publisher = {mathdoc},
     volume = {21},
     number = {3},
     year = {1983},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1983_21_3_a2/}
}
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N. P. Gushel'. On Fano varieties of genus 6. Izvestiya. Mathematics , Tome 21 (1983) no. 3, pp. 445-459. http://geodesic.mathdoc.fr/item/IM2_1983_21_3_a2/