Related papers: The weight two compactly supported Euler character…
In this paper we compute the generating function for the Euler characteristic of the Deligne-Mumford compactification of the moduli space of smooth n-pointed genus 2 curves.
For $g\ge 2$ and $n\ge 0$, let $\mathcal{H}_{g,n}\subset \mathcal{M}_{g,n}$ denote the complex moduli stack of $n$-marked smooth hyperelliptic curves of genus $g$. A normal crossings compactification of this space is provided by the theory…
The generating function for $S_n$-equivariant Euler characteristics of moduli spaces of pointed hyperelliptic curves for any genus g>1 is calculated. This answer generalizes the known ones for genera 2 and 3 and answers obtained by J.…
We study the weight 2 graded piece of the compactly supported rational cohomology of the moduli spaces of curves $M_{g,n}$ and show that this can be computed as the cohomology of a graph complex that is closely related to graph complexes…
We give a formula for the S_n - equivariant Euler characteristics of the moduli spaces of genus g curves with n marked points
We study the weight 11 part of the compactly supported cohomology of the moduli space of curves $M_{g,n}$, using graph complex techniques, with particular attention to the case $n = 0$. As applications, we prove new nonvanishing results for…
Let ${mathcal M}_g^n$ be the moduli space of n-pointed Riemann surfaces of genus g. Denote by ${\bar {\mathcal M}}_g^n$ the Deligne-Mumford compactification of ${mathcal M}_g^n$. In the present paper, we calculate the orbifold and the…
Let $\bar{\mathcal{M}}_{g, m|n}$ denote Hassett's moduli space of weighted pointed stable curves of genus $g$ for the heavy/light weight data $\left(1^{(m)}, 1/n^{(n)}\right)$, and let $\mathcal{M}_{g, m|n} \subset \bar{\mathcal{M}}_{g,…
In this short note we present a generating function computing the compactly supported Euler characteristic $\chi_c(F(X, n), K^{\boxtimes n})$ of the configuration spaces on a topologically stratified space $X$, with $K$ a constructible…
We study $\mathbb{S}_n$-equivariant weight-graded and topological Euler characteristics of the universal Picard stack $\mathrm{Pic}_{g, n}^d \to \mathcal{M}_{g, n}$ of degree-$d$ line bundles over $\mathcal{M}_{g, n}$. We prove that in the…
We prove a formula for the ${\mathbb S}_n$-equivariant Euler characteristic of the moduli space of graphs $\mathcal{MG}_{g,n}$. Moreover, we prove that the rational ${\mathbb S}_n$-invariant cohomology of $\mathcal{MG}_{g,n}$ stabilizes for…
Let $\overline{\mathscr{M}}_{g, n}$ be the moduli space of $n$-pointed stable genus $g$ curves, and let $\mathscr{M}_{g, n}$ be the moduli space of $n$-pointed smooth curves of genus $g.$ In this paper, we obtain an asymptotic expansion for…
We study the weight-graded compactly supported cohomology of the moduli spaces of curves $\mathcal{M}_{g,n}$ using the Getzler-Kapranov graph complex. After recollecting the theory and some previous results, we compute the cohomology in…
We prove an asymptotic formula for the Euler characteristic of Kontsevich's commutative graph complex. This formula implies that the total amount of commutative graph homology grows super-exponentially with the rank and, via a theorem of…
We compute the weighted Euler characteristic, equivariant with respect to the action of the symplectic group of degree six over the field of two elements, of the moduli space of principally polarized abelian threefolds together with a level…
For a smooth, projective scheme $X$ over a field $k$ or any variety $X$ if $k$ has characteristic zero, we compute the compactly supported $\mathbb{A}^1$-Euler characteristic of $\operatorname{Sym}^2(X)$ if $\operatorname{char}(k) \ne 2$…
We show that the moduli space M(r,c) of semistable sheaves on n-dimensional projective space with support of dimension one, with multiplicity r and with Euler characteristic c is isomorphic to M(r,-c).
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 sum of the corresponding weights is no greater than…
In their homonymous article, Sam Payne and Thomas Willwacher construct a combinatorial graph complex to compute the weight 11 part of the compactly supported cohomology of the moduli space of curves $\cM_{g,n}$ and compute explicitly the…
We compute the Euler characteristic with compact supports $\chi_c$ of the formal barycenter spaces with weights of a finite CW complex, connected or not. This reduces to the topological Euler characteristic $\chi$ when the weights of the…