The Chow Ring of the Stack of Smooth Plane Cubics

TL;DR

This paper provides an explicit description of the integral Chow ring for the stack of smooth plane cubics and explores relations for hypersurfaces of various dimensions and degrees.

Contribution

It offers the first explicit presentation of the Chow ring for the stack of smooth plane cubics and extends to relations in hypersurfaces of different dimensions and degrees.

Findings

Explicit presentation of the Chow ring for smooth plane cubics

Determination of relations in hypersurfaces of any dimension and degree

Foundation for further algebraic geometry research on hypersurface stacks

Abstract

We give an explicit presentation of the integral Chow ring of a stack of smooth plane cubics. We also determine some relations in the general case of hypersurfaces of any dimension and degree.