## A geometric approach to the Cohen-Lenstra heuristics by Aaron Landesman

It is well known to experts that moduli spaces exist whose integer points parameterize n-torsion elements in class groups of quadratic number fields.
In particular, counting points of bounded height on these spaces is tantamount to solving cases of the Cohen-Lenstra heuristics.
We explain why many of these moduli spaces have the following relatively simple form:
They are the quotient of the complement of a hypersurface in affine space by the action of an algebraic group.