相关论文: Moduli of regular holonomic D-modules with normal …

In this paper, we will provide constructions of D-module structures on the complex computing the periodic cyclic homology of a stable infinity-category defined over a scheme of characteristic zero. We give two methods. The first one is…

The so called theory of derived D-modules is an extension of classical D-modules to derived algebraic geometry, which uses the derived information of the base scheme. We prove that the three different definitions of derived D-modules, given…

Studying degenerations of moduli spaces of semistable principal bundles on smooth curves leads to the problem of constructing and studying moduli spaces on singular curves. In this note, we will see that the moduli spaces of…

We prove that a holonomic binomial $D$--module $M_A (I,\beta)$ is regular if and only if certain associated primes of $I$ determined by the parameter vector $\beta\in \CC^d$ are homogeneous. We further describe the slopes of $M_A(I,\beta)$…

We explain the isomorphism between the $G$-Hilbert scheme and the F-blowup from the noncommutative viewpoint after Van den Bergh. In doing this, we immediately and naturally arrive at the notion of $D$-modules. We also find, as a byproduct,…

We prove that applying a projective functor to a holonomic simple module over a semi-simple finite dimensional complex Lie algebra produces a module that has an essential semi-simple submodule of finite length. This implies that holonomic…

A method of G. Wilson for generating commutative algebras of ordinary differential operators is extended to higher dimensions. Our construction, based on the theory of D-modules, leads to a new class of examples of commutative rings of…

We establish a connection between the theory of cyclotomic ideal class groups and the theory of "geometric" Galois modules and obtain results on the Galois module structure of coherent cohomology groups of Galois covers of varieties over Z.…

This is the second in a series of two papers developing a moduli-theoretic framework for differential ideal sheaves associated with formally integrable, involutive systems of algebraic partial differential equations (PDEs). Building on…

Beilinson--Bernstein localisation relates representations of a Lie algebra $\mathfrak{g}$ to certain $\mathcal{D}$-modules on the flag variety of $\mathfrak{g}$. In [arXiv:2002.01540], examples of $\mathfrak{sl}_2$-representations which…

The subject of this paper is an algebraic version of the irregular Riemann-Hilbert correspondence which was mentioned in [arXiv:1910.09954] by the author. In particular, we prove an equivalence of categories between the triangulated…

A holomorphic triple over a compact Riemann surface consists of two holomorphic vector bundles and a holomorphic map between them. After fixing the topological types of the bundles and a real parameter, there exist moduli spaces of stable…

The Riemann-Hilbert correspondence embeds the triangulated category of (not necessarily regular) holonomic D-modules into that of $\mathbb R$-constructible enhanced ind-sheaves. The source category has a standard t-structure. Here, we…

The purpose of this paper is to initiate a new attack on Arveson's resistant conjecture, that all graded submodules of the $d$-shift Hilbert module $H^2$ are essentially normal. We introduce the stable division property for modules (and…

Let V be the space of 2x2x2 complex hypermatrices, endowed with the natural group action of GL=GL(2,C)^3. The category of GL-equivariant coherent D-modules on V is equivalent to the category of representations of a quiver with relations. In…

We study the wall-crossing of the moduli spaces $\mathbf{M}^\alpha (d,1)$ of $\alpha$-stable pairs with linear Hilbert polynomial $dm+1$ on the projective plane $\mathbb{P}^2$ as we alter the parameter $\alpha$. When $d$ is 4 and 5, at each…

We investigate the relationship between supersymmetric gauge theories with moduli spaces and matrix models. Particular attention is given to situations where the moduli space gets quantum corrected. These corrections are controlled by…

We study de Rham character sheaves on a commutative connected algebraic group $G$, defined as multiplicative line bundles with integrable connection. We construct a group algebraic space $G^\flat$ representing their moduli problem on…

In this work, we describe the moduli of triples of points in quaternionic projective space which define uniquely the congruence classes of such triples relative to the action of the isometry group of quaternionic hyperbolic space ${\rm…

The aim of this paper is two--fold. We first strongly improve our previous main result Theorem 3.1 in Arxiv 1702.00918v3 12Feb2018 ("Brill-Noether loci of rank two vector bundles on a general $\nu$-gonal curve"), concerning classification…