Corpus ID: 237940404

# A Universal Formula For Counting Cubic Surfaces

@inproceedings{Deopurkar2021AUF,
title={A Universal Formula For Counting Cubic Surfaces},
author={Anand Deopurkar and Anand Patel and Dennis Tseng},
year={2021}
}
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 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 3-fold.

#### References

SHOWING 1-10 OF 29 REFERENCES
96120: The degree of the linear orbit of a cubic surface
• Mathematics
• 2019
We compute the degree of the orbit closure of a generic cubic surface under the action of ${\rm PGL}(\mathbb{C},4)$. The result, 96120, is obtained by using methods from numerical algebraic geometry.
Geometry of complete cuspidal plane cubics
• Mathematics
• 1989
We show how to compute all fundamental numbers for plane cuspidal cubics. This updates and extends the work of Schubert on this subject. In our approach we need a far more precise description of theExpand
Automorphism groups on normal singular cubic surfaces with no parameters
The classification of normal singular cubic surfaces in P 3 over a complex number field C was given by J. W. Bruce and C. T. C. Wall. In this paper, first we prove their results by a different way,Expand
A Luna étale slice theorem for algebraic stacks
• Mathematics
• 2015
We prove that every algebraic stack, locally of finite type over an algebraically closed field with affine stabilizers, is etale-locally a quotient stack in a neighborhood of a point with a linearlyExpand
Linear orbits of smooth plane curves
• Mathematics
• 1992
The group PGL(3) of linear transformations of the projective plane acts naturally on the projective space parametrizing curves of a given degree. In this note we begin the study of the orbits ofExpand
Towards the degree of the PGL(4)-orbit of a cubic surface
• Physics
• 2020
We study the action of the group PGL(4) on the parameter space P19 of complex cubic surfaces. Specifically, we look at how the techniques used by Aluffi and Faber in [1] can be extended to computeExpand
Moduli of cubic surfaces and their anticanonical divisors
• Mathematics
• Revista Matemática Complutense
• 2019
We consider the moduli space of log smooth pairs formed by a cubic surface and an anticanonical divisor. We describe all compactifications of this moduli space which are constructed using geometricExpand
Moduli spaces of weighted pointed stable curves
Abstract A weighted pointed curve consists of a nodal curve and a sequence of marked smooth points, each assigned a number between zero and one. A subset of the marked points may coincide if the sumExpand
On the local quotient structure of Artin stacks
Abstract We show that near closed points with linearly reductive stabilizer, Artin stacks are formally locally quotient stacks by the stabilizer. We conjecture that the statement holds etale locallyExpand
Equivariant intersection theory
• Mathematics
• 1996
In this paper we develop an equivariant intersection theory for actions of algebraic groups on algebraic schemes. The theory is based on our construction of equivariant Chow groups. They areExpand