相关论文: Cohomology of moduli space of cubic fourfolds I

We study categories of d-dimensional cobordisms from the perspective of Tillmann and Galatius-Madsen-Tillmann-Weiss. There is a category $C_\theta$ of closed smooth (d-1)-manifolds and smooth d-dimensional cobordisms, equipped with…

In this paper we consider moduli spaces of coherent systems on an elliptic curve. We compute their Hodge polynomials and determine their birational types in some cases. Moreover we prove that certain moduli spaces of coherent systems are…

We study the moduli space of four dimensional ordinary Lie algebras, and their versal deformations. Their classification is well known; our focus in this paper is on the deformations, which yield a picture of how the moduli space is…

The Betti numbers of moduli spaces of representations of a universal central extension of a surface group in the groups U(2,1) and SU(2,1) are calculated. The results are obtained using the identification of these moduli spaces with moduli…

The moduli space of regular stable maps with values in a complex manifold admits naturally the structure of a complex orbifold. Our proof uses the methods of differential geometry rather than algebraic geometry. It is based on Hardy…

In this paper, we study the moduli space of all complex 5-dimensional Lie algebras, realizing it as a stratification by orbifolds, which are connected by jump deformations. The orbifolds are given by the action of finite groups on very…

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.

We show that the integral cohomology rings of the moduli spaces of stable rational marked curves are Koszul. This answers an open question of Manin. Using the machinery of Koszul spaces developed by Berglund, we compute the rational…

In these notes, we introduce various approaches (GIT, Hodge theory, and KSBA) to constructing and compactifying moduli spaces. We then discuss the pros and cons for each approach, as well as some connections between them.

Let $\mathbf{M}_n$ be the Simpson compactification of twisted ideal sheaves $\mathcal{I}_{L,Q}(1)$ where $Q$ is a rank $4$ quardric hypersurface in $\mathbb{P}^n$ and $L$ is a linear subspace of dimension $n-2$. This paper calculates the…

In this paper, we give a classification of the 3-dimensional associative algebras over the complex numbers, including a construction of the moduli space, using versal deformations to determine how the space is glued together.

We continue the analysis of the geometry of generic Minkowski $\mathcal{N} = 1$, $D = 4$ flux compactifications in M-theory using exceptional generalised geometry, including the calculation of the infinitesimal moduli spaces. The…

In this paper, we study the moduli space of $1|2$-dimensional complex associative algebras, which is also the moduli space of codifferentials on the tensor coalgebra of a $2|1$-dimensional complex space. We construct the moduli space by…

In this paper, we study the moduli space of quasi-polarized complex K3 surfaces of degree 6 and 8 via geometric invariant theory. The general members in such moduli spaces are complete intersections in projective spaces and we have natural…

In this paper, we study moduli spaces of representations of certain quivers with relations. For quivers without relations and other categories of homological dimension one, a lot of information is known about the cohomology of their moduli…

We give a concrete method to explicitly compute the rational cohomology of the unordered configuration spaces of connected, oriented, closed, even-dimensional manifolds of finite type which we have implemented in Sage [S+09]. As an…

We compute the intersection cohomology of the moduli spaces $M_{r,d}$ of semistable vector bundles having rank $r$ and degree $d$ over a curve. We do this by relating the Hodge-Deligne polynomial of the intersection cohomology of $M_{r,d}$…

We study the moduli space of Higgs bundles on a compact Riemann surface. It was shown by Thaddeus and Hausel (in rank 2) and Markman (in general rank) that the rational cohomology ring of this space is generated by universal classes. In…

Let X be a compact connected Riemann surface of genus at least two. We compute the Chen--Ruan cohomology ring of the moduli space of stable PSL(2, C)--bundles of nontrivial second Stiefel--Whitney class over X.

The real points of the Deligne-Knudsen-Mumford moduli space of marked points on the sphere has a natural tiling by associahedra. We extend this idea to create a moduli space tiled by cyclohedra. We explore the structure of this space,…