3 research outputs found
The class of the locus of intermediate Jacobians of cubic threefolds
We study the locus of intermediate Jacobians of cubic threefolds within the
moduli space of complex principally polarized abelian fivefolds, and its
generalization to arbitrary genus - the locus of abelian varieties with a
singular odd two-torsion point on the theta divisor. Assuming that this locus
has expected codimension (which we show to be true for genus up to 5), we
compute the class of this locus, and of is closure in the perfect cone toroidal
compactification, in the Chow, homology, and the tautological ring.
We work out the cases of genus up to 5 in detail, obtaining explicit
expressions for the classes of the closures of the locus of products of an
elliptic curve and a hyperelliptic genus 3 curve, in moduli of principally
polarized abelian fourfolds, and of the locus of intermediate Jacobians in
genus 5. In the course of our computation we also deal with various
intersections of boundary divisors of a level toroidal compactification, which
is of independent interest in understanding the cohomology and Chow rings of
the moduli spaces.Comment: v2: new section 9 on the geometry of the boundary of the locus of
intermediate Jacobians of cubic threefolds. Final version to appear in
Invent. Mat