A universal formula for counting cubic surfaces

Deopurkar, Anand; Patel, Anand; Tseng, Dennis

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A universal formula for counting cubic surfaces

Date

2026

Authors

Deopurkar, Anand

Patel, Anand

Tseng, Dennis

Abstract

Using 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.

Keywords

cubic surfaces, enumerative geometry, equivariant geometry, moduli theory

URI

https://hdl.handle.net/1885/733814255

Collections

ANU Research Publications

Source

Algebraic Geometry

Type

Journal article

Entity type

Publication

DOI

10.14231/AG-2026-012

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A universal formula for counting cubic surfaces

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