%0 Journal Article
%T The abelian fibration on the Hilbert cube of a K3 surface of genus 9
%A Atanas Iliev
%A Kristian Ranestad
%J Mathematics
%D 2005
%I arXiv
%X In this paper we construct an abelian fibration over ${\bf P}^3$ on the Hilbert cube of the primitive K3 surface of genus 9. After the abelian fibration constructed by Mukai on the Hilbert square on the primitive K3 surface S of genus 5, this is the second example where the abelian fibration on such Hilb_n(S) is directly constructed. Our example is also the first known abelian fibration on a Hilbert scheme Hilb_n(S) of a primitive K3 surface S which is not the Hilbert square of S; the primitive K3 surfaces on the Hilbert square of which such a fibration exists are known by a recent result of Hassett and Tschinkel.
%U http://arxiv.org/abs/math/0507016v1