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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