3 citations · 5 across the 6 of their papers we have counts for
12 papers
The abelian fibration on the Hilbert cube of a K3 surface of genus 9
Atanas Iliev, Kristian Ranestad
In this paper we construct an abelian fibration over on the Hilbert cube of the primitive K3 surface of genus 9. After the abelian fibration constructed by Mukai on the…
Pfaffian Lines and Vector Bundles on Fano Threefolds of Genus 8
Atanas Iliev, Laurent Manivel
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 Chow ring of the Cayley plane
Atanas Iliev, Laurent Manivel
We give a full description of the Chow ring of the complex Cayley plane, the simplest of the exceptional flag varieties. We describe explicitely the most interesting of its Schuber…
Severi varieties and their varieties of reductions
Atanas Iliev, Laurent Manivel
We study the varieties of reductions associated to the four Severi varieties, the first example of which is the Fano threefold of index 2 and degree 5 studied by Mukai and others.…
Elliptic curves and rank-2 vector bundles on the prime Fano threefold of genus 7
A. Iliev, D. Markushevich
According to Mukai, any prime Fano threefold X of genus 7 is a linear section of the spinor tenfold in the projectivized half-spinor space of Spin(10). It is proven that the moduli…
The Sp3-grassmannian and duality for prime Fano threefolds of genus 9
Atanas Iliev
By a result of Mukai, the non-abelian Brill-Noether locus X = M_C(2,K:3F) of type II, defined by a stable rank 2 vector bundle F of invariant 3 over a plane quartic curve C, is a p…