Fano threefolds of genus 6

This paper was written in 1982. Ideas and methods of “Clemens C.H., Griffiths Ph. The intermediate Jacobian of a cubic threefold” are applied to a Fano threefold X of genus 6 – intersection of Grassmann sixfold with two hyperplanes and a quadric. We prove:

1. The Fano surface F(X) of X is smooth and irreducible. Hodge numbers and some other invariants of F(X) are calculated.
2. Tangent bundle theorem for X, and its geometric interpretation. It is shown that F(X) defines X uniquely.
3. The Abel - Jacobi map from the Albanese of F(X) to the middle Jacobian of X is an isogeny.