Smoothness and singularities of the perfect form and the second Voronoi compactification of ${\mathcal{A}}_g$

Mathieu Dutour Sikirić, Klaus Hulek, Achill Schürmann

We study the cones in the first Voronoi or perfect cone decomposition of quadratic forms with respect to the question which of these cones are basic or simplicial. As a consequence…