BIRS Workshop Lecture Videos
On the moduli space of cubic threefolds and of some hyperkähler manifolds Sarti, Alessandra
In a famous paper Allcock, Carlson and Toledo describe the moduli space of smooth cubic threefolds as a 10-dimensional ball quotient. We show how the 10-dimensional ball quotient is also the moduli space of hyperkähler fourfolds deformation equivalent to the Hilbert scheme of two points on a K3 surface with non-symplectic automorphism of order three (not coming from the K3 surface). With the help of the ball quotient we completely describe the hyperkähler manifolds and we identify them with the Fano variety of lines of cubic fourfolds that are triple covers of a smooth cubic threefold. As a consequence we give a relation between the hyperkähler manifolds and the moduli space of genus five principally polarized abelian varieties.
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