# Intersections of loci of admissible covers with tautological classes

@article{Schmitt2020IntersectionsOL, title={Intersections of loci of admissible covers with tautological classes}, author={Johannes Schmitt and Jason van Zelm}, journal={Selecta Mathematica}, year={2020} }

<jats:p>For a finite group <jats:italic>G</jats:italic>, let <jats:inline-formula><jats:alternatives><jats:tex-math>$$\overline{\mathcal {H}}_{g,G,\xi }$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:msub>
<mml:mover>
<mml:mi>H</mml:mi>
<mml:mo>¯</mml:mo>
</mml:mover>
<mml:mrow>
<mml:mi>g</mml:mi…

## 26 Citations

The $${\mathcal {H}}$$-tautological ring

- MathematicsSelecta Mathematica
- 2021

We extend the theory of tautological classes on moduli spaces of stable curves to the more general setting of moduli spaces of admissible Galois covers of curves, introducing the so-called…

Tropical double ramification loci

- Mathematics
- 2019

Motivated by the realizability problem for principal tropical divisors with a fixed ramification profile, we explore the tropical geometry of the double ramification locus in…

Chow rings of stacks of prestable curves I

- MathematicsForum of Mathematics, Sigma
- 2022

Abstract We study the Chow ring of the moduli stack
$\mathfrak {M}_{g,n}$
of prestable curves and define the notion of tautological classes on this stack. We extend formulas for intersection…

HIGHER GENUS GROMOV–WITTEN THEORY OF $\mathsf{Hilb}^{n}(\mathbb{C}^{2})$ AND $\mathsf{CohFTs}$ ASSOCIATED TO LOCAL CURVES

- MathematicsForum of Mathematics, Pi
- 2019

We study the higher genus equivariant Gromov–Witten theory of the Hilbert scheme of $n$ points of $\mathbb{C}^{2}$ . Since the equivariant quantum cohomology, computed by Okounkov and Pandharipande…

The H-tautological ring

- Mathematics
- 2020

We extend the theory of tautological classes on moduli spaces of stable curves to the more general setting of moduli spaces of admissible Galois covers of curves, introducing the so-called…

PROPERTIES OF TAUTOLOGICAL CLASSES AND THEIR INTERSECTIONS Submitted by

- Mathematics
- 2019

PROPERTIES OF TAUTOLOGICAL CLASSES AND THEIR INTERSECTIONS The tautological ring of the moduli space of curves is an object of interest to algebraic geometers in Gromov-Witten theory and enumerative…

Non-tautological Hurwitz cycles

- MathematicsMathematische Zeitschrift
- 2021

We show that various loci of stable curves of sufficiently large genus admitting degree d covers of positive genus curves define non-tautological algebraic cycles on $${\overline{{\mathcal…

Zero cycles on the moduli space of curves

- MathematicsÉpijournal de Géométrie Algébrique
- 2020

While the Chow groups of 0-dimensional cycles on the moduli spaces of
Deligne-Mumford stable pointed curves can be very complicated, the span of the
0-dimensional tautological cycles is always of…

Abelian tropical covers

- Mathematics
- 2019

The goal of this article is to classify unramified covers of a fixed tropical base curve $\Gamma$ with an action of a finite abelian group G that preserves and acts transitively on the fibers of the…

Generalized Tevelev degrees of $\mathbb{P}^1$

- Mathematics
- 2021

Let (C , p1, . . . , pn ) be a general curve. We consider the problem of enumerating covers of the projective line by C subject to incidence conditions at the marked points. These counts have been…

## References

SHOWING 1-10 OF 81 REFERENCES

Classes of Weierstrass points on genus 2 curves

- Computer ScienceTransactions of the American Mathematical Society
- 2019

The codimension is studied to establish distinct marked Weierstrass points inside the moduli space of genus and to describe the classes of the closure of these loci of stable curves.

Tautological rings of spaces of pointed genus two curves of compact type

- MathematicsCompositio Mathematica
- 2016

We prove that the tautological ring of ${\mathcal{M}}_{2,n}^{\mathsf{ct}}$ , the moduli space of $n$ -pointed genus two curves of compact type, does not have Poincaré duality for any $n\geqslant 8$ .…

The Gorenstein conjecture fails for the tautological ring of $\mathcal{\overline{M}}_{2,n}$

- Mathematics
- 2012

We prove that for N equal to at least one of the integers 8, 12, 16, 20 the tautological ring $R^{\bullet}(\overline {\mathcal {M}}_{2,N})$ is not Gorenstein. In fact, our N equals the smallest…

Moduli of $G$-covers of curves: geometry and singularities

- Mathematics
- 2019

In a recent paper Chiodo and Farkas described the singular locus and the locus of non-canonical singularities of the moduli space of level curves. In this work we generalize their results to the…

Nontautological Bielliptic Cycles

- Mathematics
- 2016

Let $[\overline{\mathcal{B}}_{2,0,20}]$ and $[\mathcal{B}_{2,0,20}]$ be the classes of the loci of stable resp. smooth bielliptic curves with 20 marked points where the bielliptic involution acts on…

Boundary of the pyramidal equisymmetric locus of
$${\mathcal M}_n$$
M
n

- Mathematics
- 2020

The augmented moduli space $$\widehat{\mathcal M}_n$$ M ^ n is a compactification of moduli space $$\mathcal M_n$$ M n obtained by adding stable hyperbolic surfaces. The different topological types…

HIGHER GENUS GROMOV–WITTEN THEORY OF $\mathsf{Hilb}^{n}(\mathbb{C}^{2})$ AND $\mathsf{CohFTs}$ ASSOCIATED TO LOCAL CURVES

- MathematicsForum of Mathematics, Pi
- 2019

We study the higher genus equivariant Gromov–Witten theory of the Hilbert scheme of $n$ points of $\mathbb{C}^{2}$ . Since the equivariant quantum cohomology, computed by Okounkov and Pandharipande…

The Enumerative Geometry of Double Covers of Curves

- Mathematics
- 2018

Let Adm(g, h)_2m be the space of admissible double covers C → D of curves of genus g and h, with all the ramification and branch points of C and D marked, and where the covering involution permutes…

Limit points of the branch locus of 𝓜g

- MathematicsAdvances in Geometry
- 2019

Abstract Let 𝓜g be the moduli space of compact connected hyperbolic surfaces of genus g ≥ 2, and 𝓑g ⊂ 𝓜g its branch locus. Let Mg^ $\begin{array}{} \widehat{{\mathcal{M}}_{g}} \end{array} $ be the…

Pointed admissible G-covers and G-equivariant cohomological field theories

- MathematicsCompositio Mathematica
- 2005

For any finite group G we define the moduli space of pointed admissible G-covers and the concept of a G-equivariant cohomological field theory (G-CohFT), which, when G is the trivial group, reduces…