Related papers: Periods on the moduli space of genus 0 curves

The cohomology groups of line bundles over complex tori (or abelian varieties) are classically studied invariants of these spaces. In this article, we compute the cohomology groups of line bundles over various holomorphic, non-commutative…

We give a formula for the Eisenstein cohomology of local systems on the partial compactification of the moduli of principally polarized abelian varieties given by rank 1 degenerations. For genus 2 we give a formula for the full Eisenstein…

We prove a general formula for the intersection form of two arbitrary monomials in boundary divisors. Furthermore we present a tree basis of the cohomology of $\overline {M}_{0,n}$. With the help of the intersection form we determine the…

In this article, we introduce the notion of periodic de Rham bundles over smooth complex curves. We prove that motivic de Rham bundles over smooth complex curves are periodic. We conjecture that irreducible periodic de Rham bundles over…

We survey recent progress on the cohomology of moduli spaces of stable curves through the lens of the Hodge and Tate conjectures, especially their generalized coniveau forms, which relate Hodge structures and l-adic Galois representations…

In this paper we compute the cohomology of certain special cases of nilpotent algebras in a complex \zt-graded vector space of arbitrary finite dimension. These algebras are generalizations of the only two nontrivial complex 2-dimensional…

The motivation of this work is to define cohomology classes in the space of knots that are both easy to find and to evaluate, by reducing the problem to simple linear algebra. We achieve this goal by defining a combinatorial graded cochain…

A method of constructing Cohomological Field Theories (CohFTs) with unit using minimal classes on the moduli spaces of curves is developed. As a simple consequence, CohFTs with unit are found which take values outside of the tautological…

In this note it is shown that associating to a principally polarized abelian variety its de Rham cohomology defines a faithfully flat morphism of the moduli space of principally polarized abelian varieties in positive characteristics to the…

We construct Hida and Coleman theories for the degree 0 and 1 cohomology of automorphic line bundles on the modular curve and we define a p-adic duality pairing between the theories in degree 0 and 1.

The rational homology of unordered configuration spaces of points on any surface was studied by Drummond-Cole and Knudsen. We compute the rational cohomology of configuration spaces on a closed orientable surface, keeping track of the mixed…

We describe the Chow rings of moduli spaces of ordered configurations of points on the projective line for arbitrary (sufficiently generic) stabilities. As an application, we exhibit such a moduli space admitting two small…

In this expository article we give a categorical definition of the integral cohomology ring of a stack. We show that for quotient stacks the categorical cohomology may be identified with equivariant cohomology. Via this identification we…

The moduli space of slope-stable vector bundles on a normal projective variety over an algebraically closed field of characteristic $p\geq 0$ is stratified with respect to the decomposition type. On a smooth projective curve of genus at…

We compute the rational cohomology of the moduli space $\mathcal{M}_{4,1}$ of non-singular genus $4$ curves with $1$ marked point, using Gorinov-Vassiliev's method.

The space of smooth rational curves of degree $d$ in a projective variety $X$ has compactifications by taking closures in the Hilbert scheme, the moduli space of stable sheaves or the moduli space of stable maps respectively. In this paper…

In this review, novel non-standard techniques for the computation of cohomology classes on toric varieties are summarized. After an introduction of the basic definitions and properties of toric geometry, we discuss a specific computational…

The moduli space $M_g^{trop}$ of tropical curves of genus $g$ is a generalized cone complex that parametrizes metric vertex-weighted graphs of genus $g$. For each such graph $\Gamma$, the associated canonical linear system $\vert…

In this article we give a survey of homology computations for moduli spaces $\mathfrak{M}_{g,1}^m$ of Riemann surfaces with genus $g\geqslant 0$, one boundary curve, and $m\geqslant 0$ punctures. While rationally and stably this question…

We bound from below the complexity of the top Chern class of the Hodge bundle in the Chow ring of the moduli space of curves: no formulas in terms of classes of degrees 1 and 2 can exist. As a consequence of the Torelli map, the 0-section…