# The integral Chow ring of the stack of smooth non-hyperelliptic curves of genus three

@article{DiLorenzo2020TheIC, title={The integral Chow ring of the stack of smooth non-hyperelliptic curves of genus three}, author={Andrea Di Lorenzo and Damiano Fulghesu and Angelo Vistoli}, journal={arXiv: Algebraic Geometry}, year={2020} }

We compute the integral Chow ring of the stack of smooth, non-hyperelliptic curves of genus three. We obtain this result by computing the integral Chow ring of the stack of smooth plane quartics, by means of equivariant intersection theory.

## 7 Citations

The integral Chow rings of moduli of Weierstrass fibrations

- Mathematics
- 2022

. We compute the Chow rings with integral coeﬃcients of moduli stacks of minimal Weierstrass ﬁbrations over the projective line. For each integer N ≥ 1, there is a moduli stack W min N parametrizing…

The integral Chow ring of $\mathcal{M}_{0}(\mathbb{P}^r, d)$, for $d$ odd

- Mathematics
- 2022

For any odd integer d, we give a presentation for the integral Chow ring of the stack M0(P, d), as a quotient of the polynomial ring Z[c1, c2]. We describe an efficient set of generators for the…

Intersection theory on moduli of smooth complete intersections

- Mathematics
- 2022

We provide a general method for computing rational Chow rings of moduli of smooth complete intersections. We specialize this result in different ways: to compute the integral Picard group of the…

Stable cuspidal curves and the integral Chow ring of $\overline{\mathscr{M}}_{2,1}$

- Mathematics
- 2021

In this paper we introduce the moduli stack M̃g,n of n-marked stable at most cuspidal curves of genus g and we use it to determine the integral Chow ring of M 2,1. Along the way, we also determine…

Equivariant Chow-Witt groups and moduli stacks of elliptic curves

- Mathematics, Computer Science
- 2021

The Chow-Witt ring of the moduli stack of stable (resp. smooth) elliptic curves is computed, providing a geometric interpretation of the new generators.

The Chow rings of the moduli spaces of curves of genus 7, 8, and 9

- Mathematics
- 2021

The rational Chow ring of the moduli space Mg of curves of genus g is known for g ≤ 6. Here, we determine the rational Chow rings of M7,M8, and M9 by showing they are tautological. One key ingredient…

Polarized twisted conics and moduli of stable curves of genus two

- Mathematics
- 2021

In this paper we introduce the stack of polarized twisted conics and we use it to give a new point of view on M2. In particular, we present a new and independent approach to the computation of the…

## References

SHOWING 1-10 OF 25 REFERENCES

The Chow Ring of the Stack of Hyperelliptic Curves of Odd Genus

- Mathematics, GeologyInternational Mathematics Research Notices
- 2019

We find a new presentation of the stack of hyperelliptic curves of odd genus as a quotient stack and we use it to compute its integral Chow ring by means of equivariant intersection theory.

The integral Chow ring of the stack of hyperelliptic curves of even genus

- Mathematics
- 2007

Let $g$ be an even positive integer. In this paper we compute the integral Chow ring of the stack of smooth hyperelliptic curves of genus $g$.

The Integral Chow Ring of the Stack of at Most 1-Nodal Rational Curves

- Mathematics
- 2006

We give a presentation for the stack of rational curves with at most 1 node as the quotient by GL3 of an open set in a 6-dimensional irreducible representation. We then use equivariant intersection…

The Chow Ring of the Stack of Smooth Plane Cubics

- Mathematics
- 2016

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.

The Chow Ring of the Moduli Space of Curves of Genus 5

- Mathematics
- 1995

Let M g be the moduli spare of smooth curves of genus g over an algebraically closed field (of characteristic differetd, from 2 and 3) and let \({\bar M_g}\) be its compactification by…

Picard group of moduli of curves of low genus in positive characteristic

- Mathematics
- 2020

We compute the Picard group of the moduli stack of smooth curves of genus g for $$3\le g\le 5$$ 3 ≤ g ≤ 5 , using methods of equivariant intersection theory. We base our proof on the computation of…

The Integral Chow Ring of $\bar{M}_2$

- Mathematics
- 2019

In this paper we compute the Chow ring of the moduli stack $\bar{M}_2$ of stable curves of genus 2 with integral coefficients.

The Chow ring of the moduli space of curves of genus six

- Mathematics
- 2013

We determine the Chow ring (with Q-coecients) of M6 by showing that all Chow classes are tautological. (In particular, all algebraic cohomology is tautological, and the natural map from Chow to…

Localization in equivariant intersection theory and the Bott residue formula

- Mathematics
- 1995

We prove the localization theorem for torus actions in equivariant intersection theory. Using the theorem we give another proof of the Bott residue formula for Chern numbers of bundles on smooth…

Chow rings of moduli spaces of curves II: Some results on the Chow ring of $\overline{\mathscr{M}}_4$

- Mathematics
- 1990

ring of the moduli space of stable curves of genus 4. These results are not complete. We find generators for the Chow ring of 4 and for the Chow groups in codimension 1 and 2 of -W4. For A2(G'4) we…