A Universal Formula For Counting Cubic Surfaces

Anand Deopurkar; Anand Patel; Dennis Tseng

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A Universal Formula For Counting Cubic Surfaces

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arxiv 2109.12672 v1 pith:MVTWQTJK submitted 2021-09-26 math.AG

Anand Deopurkar , Anand Patel , Dennis Tseng This is my paper · ORCID

classification math.AG

keywords cubicgeneralsurfacearisesformulatimesuniversalapplications

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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.

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