Pfaffian Lines and Vector Bundles on Fano Threefolds of Genus 8
By A. Iliev, Laurent Manivel. 2005
113 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/8a4199975fe08ab3eb710e546e2f8575aac9d351
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Citations in the corpus
- Hilbert schemes of lines and conics and automorphism groups of Fano threefolds (2016, background): “some authors prefer to consider only general Fano varieties in the corresponding families (see e.g. [Ili03]). On the other hand, for the applications to Cremona groups (cf. [Pro12], [Pro11], [Pro14], [Pro15]) one needs to consider some particular varieties. This is why we are trying to put our argum”
- Rank 2 arithmetically Cohen–Macaulay bundles on a nonsingular cubic surface (2005, methodology): “For a classification and the study of moduli spaces of aCM 2-bundles in this case, we refer to the papers [AC00,Dru00,IM00a,Fae05] (for the case i = 2), and [IM00b,Mad02,AF06, IM07 ,BF07] (for the case i = 1). We mention also [AG99], for the case of the Grassmann variety G(P1, P4).”