Deopurkar, AnandPatel, AnandTseng, Dennis2026-08-132026-08-132313-1691https://hdl.handle.net/1885/733814255Using equivariant geometry, we find a universal formula that computes the number of times a general cubic surface arises in a family. As sample applications, we show that the PGL4 orbit closure of a generic cubic surface has degree 96120, and that a general cubic surface arises 42120 times as a hyperplane section of a general cubic threefold.Anand D. thanks the Australian Research Council for the grant DE180101360 that supported a part of this project.40enPublisher Copyright: © The Author(s), 2026.cubic surfacesenumerative geometryequivariant geometrymoduli theory202610.14231/AG-2026-012105036425129