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arXiv · 2109.12672

A Universal Formula For Counting Cubic Surfaces

Anand Deopurkar·Anand Patel·Dennis Tseng
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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.

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Anand Deopurkar, Anand Patel, Dennis Tseng. 2021-09-26. A Universal Formula For Counting Cubic Surfaces. https://arxiv.org/abs/2109.12672

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