Related papers: Matrx Models: a Way to Quantum Moduli Spaces

Let $\ell$ be a length function on a group $G$, and let $M_{\ell}$ denote the operator of pointwise multiplication by $\ell$ on $\bell^2(G)$. Following Connes, $M_{\ell}$ can be used as a ``Dirac'' operator for $C_r^*(G)$. It defines a…

I will present an explicit formula for the intersection indices of the Chern classes of an arbitrary reductive group with hypersurfaces. This formula has the following applications. First, it allows to compute explicitly the Euler…

Let G be a finite group of exponent m and let k be a field of characteristic prime to m, containing the m-th roots of unity. For any Rost cycle module M over k, we construct exact sequences detecting the unramified elements in Serre's group…

In earlier papers arXiv:0802.3120, arXiv:0806.0463 of this series we constructed a sequence of intermediate moduli spaces $\bM^m(c)$ connecting a moduli space $M(c)$ of stable torsion free sheaves on a nonsingular complex projective surface…

After a short exposition of the basic properties of the tautological ring of the moduli space of genus g Deligne-Mumford stable curves with n markings, we explain three methods of detecting non-tautological classes in cohomology. The first…

Let $\Bbbk$ be an algebraically closed field, $Q$ a finite quiver, and denote by $\mathop{\mathrm{rep}}_Q^{\mathbf{d}}$ the affine $\Bbbk$-scheme of representations of $Q$ with a fixed dimension vector ${\mathbf{d}}$. Given a representation…

We construct a quantization of the moduli space $\mathcal{GH}_\Lambda(S\times\mathbb{R})$ of maximal globally hyperbolic Lorentzian metrics on $S\times \mathbb{R}$ with constant sectional curvature $\Lambda$, for a punctured surface $S$.…

Let $\mathcal{M}_{n,2n+2}$ be the coarse moduli space of CY manifolds arising from a crepant resolution of double covers of $\mathbb{P}^n$ branched along $2n+2$ hyperplanes in general position. We show that the monodromy group of a good…

The purpose of these notes is to give an introduction to Deligne-Mumford stacks and their moduli spaces, with emphasis on the moduli problem for curves. The paper has 4 sections. In section 1 we discuss the general problem of constructing a…

Let $X$ be a smooth projective variety of dimension $d$ over an algebraically closed field $k$. The main goal of this paper is to study, in the context of Voevodsky's triangulated category of motives $DM_k$, the group…

Matrix models with continuous symmetry are powerful tools for studying quantum gravity and holography. Tensor models have also found applications in holographic quantum gravity. Matrix models with discrete permutation symmetry have been…

We resolve pathological wall-crossing phenomena for moduli spaces of sheaves on higher-dimensional base manifolds. This is achieved by considering slope-semistability with respect to movable curves rather than divisors. Moreover, given a…

We study the quantum connection of product varieties in the framework of quantum cohomology. Our first main result shows that, near the origin of the Novikov variables, the quantum spectrum of \(X \times Y\) converges to the set of pairwise…

We define and study the stack ${\mathcal U}^{ns,a}_{g,g}$ of (possibly singular) projective curves of arithmetic genus g with g smooth marked points forming an ample non-special divisor. We define an explicit closed embedding of a natural…

In this article, we establish results concerning the cohomology of Zariski dense subgroups of solvable linear algebraic groups. We show that for an irreducible solvable $\mathbb{Q}$-defined linear algebraic group $\mathbf{G}$, there exists…

We give a purely algebraic construction of a cohomological field theory associated with a quasihomogeneous isolated hypersurface singularity W and a subgroup G of the diagonal group of symmetries of W. This theory can be viewed as an…

Let $C$ be a smooth projective curve of genus 0. Let $\CB$ be the variety of complete flags in an $n$-dimensional vector space $V$. Given an $(n-1)$-tuple $\alpha\in\BN[I]$ of positive integers one can consider the space $\CQ_\alpha$ of…

Let M and N be even-dimensional oriented real manifolds, and $u:M \to N$ be a smooth mapping. A pair of complex structures at M and N is called u-compatible if the mapping u is holomorphic with respect to these structures. The quotient of…

We develop a calculus based on graph enumeration for $S_n$-equivariant motivic invariants of graphically stratified moduli spaces. We apply our theory to the Deligne--Mumford moduli space $\overline{\mathcal{M}}_{g, n}$ and to the space of…

We define the Chern map from the Grothendieck group of a linear category C to the de Rham cohomology of C with coefficients in a DG-category. In order to achieve our goal, we define the notion of connection on a C-module, and we show that…