English

A Universal Formula For Counting Cubic Surfaces

Algebraic Geometry 2021-09-28 v1

Abstract

Using equivariant geometry, we find a universal formula that computes the number of times a general cubic surface arises in a family. As applications, we show that the PGL(4) 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 3-fold.

Keywords

Cite

@article{arxiv.2109.12672,
  title  = {A Universal Formula For Counting Cubic Surfaces},
  author = {Anand Deopurkar and Anand Patel and Dennis Tseng},
  journal= {arXiv preprint arXiv:2109.12672},
  year   = {2021}
}

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R2 v1 2026-06-24T06:20:53.520Z