Pfaffian lines and vector bundles on Fano threefolds of genus 8
Résumé
Let $X$ be a general complex Fano threefold of genus 8. We prove that the moduli space of rank two semistable sheaves on $X$ with Chern numbers $c_1=1$, $c_2=6$ and $c_3=0$ is isomorphic to the Fano surface $F(X)$ of conics on $X$. This surface is smooth and isomorphic to the Fano surface of lines in the orthogonal to $X$ cubic threefold. Inside $F(X)$, the non-locally free sheaves are parameterized by a smooth curve of genus 26 isomorphic to the base of the family of lines on X.
Domaines
Géométrie algébrique [math.AG]
Origine : Fichiers produits par l'(les) auteur(s)
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