Fano threefolds of genus 6
Algebraic Geometry
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/0407147,
title = {Fano threefolds of genus 6},
author = {Dmitry Logachev},
journal= {arXiv preprint arXiv:math/0407147},
year = {2007}
}
Comments
50 pages