The curve of lines on a prime Fano threefold of genus 8

Details The curve of lines on a prime Fano threefold of genus 8 The curve of lines on a prime Fano threefold of genus 8

2008-11-04

arxiv.org/abs/0811.0523v3

Mathematics

Algebraic Geometry

24 pages, misprints corrected, to appear in International Journal of Mathematics

Scientific paper

We show that a general prime Fano threefold X of genus 8 can be reconstructed
from the pair $(\Gamma,L)$, where $\Gamma$ is its Fano curve of lines and
$L=O_{\Gamma}(1)$ is the theta-characteristic which gives a natural embedding
$\Gamma \subset \matbb{P}^5$.

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