Related papers: D-modules and projective stacks

We generalise the techniques of semistable reduction for flat families of sheaves to the setting of the derived category $D^b(X)$ of coherent sheaves on a smooth projective three-fold $X$. Then we construct the moduli of PT-semistable…

A left $R$-module $M$ is called two-degree Ding projective if there exists an exact sequence $...\longrightarrow D_{1}\longrightarrow D_{0}\longrightarrow D_{-1}\longrightarrow D_{-2}\longrightarrow...$ of Ding projective left $R$-modules…

We overview numerous algorithms in computational $D$-module theory together with the theoretical background as well as the implementation in the computer algebra system \textsc{Singular}. We discuss new approaches to the computation of…

The goal of this note is to introduce an interesting question proposed by D. Rydh on an analytic version of the local structure of Artin stacks saying that near points with linearly reductive stabilizers, Artin stacks are \'etale-locally…

We prove the basic properties of determinantal semi-invariants for presentation spaces over any finite dimensional hereditary algebra over any field. These include the virtual generic decomposition theorem, stability theorem and the…

Let R be a commutative ring and C a semidualizing R-module. In this article, we introduce and investigate the notion of DC-projective complexes. We first prove that a complex X is DC-projective if and only if each degree of X is a…

We study the rank of the modular curve $X_0(49)$ over quadratic extensions. Assuming the Birch and Swinnerton-Dyer Conjecture, we show that the rank over $\mathbb{Q}(\sqrt{d})$ is positive if and only if the number of solutions of two…

We show the existence of semiorthogonal decompositions of Donaldson-Thomas categories for $(-1)$-shifted cotangent derived stacks associated with $\Theta$-stratifications on them. Our main result gives an analogue of window theorem for…

We study stacks of slope-semistable twisted sheaves on orbisurfaces with projective coarse spaces and prove that in certain cases they have many of the asymptotic properties enjoyed by the moduli of slope-semistable sheaves on smooth…

For a smooth affine algebraic group $G$, one can attach various D-module categories to it that admit convolution monoidal structure. We consider the derived category of D-modules on $G$, the stack $G/G_{ad}$ and the category of…

Let $G$ be a simple and simply connected complex Lie group. We discuss the moduli space of holomorphic semistable principal $G$ bundles over an elliptic curve $E$. In particular we give a new proof of a theorem of Looijenga and…

On a smooth projective variety with k ample line bundles, we denote by Z the complete intersection subvariety defined by generic sections. We define the twisted quantum D-module which is a vector bundle with a flat connection, a flat…

The main goal of this paper is to prove the Schmidt--Kolchin conjecture. This conjecture says the following: the vector space of degree \(d\) differentially homogeneous polynomials in \((N+1)\) variables is of dimension \((N+1)^{d}\). Next,…

Let G be a simple simply-connected group over an algebraically closed field k, X be a smooth connected projective curve over k. In this paper we develop the theory of geometric Eisenstein series on the moduli stack Bun_G of G-torsors on X…

In this paper we prove two results pertaining to the (unramified and global) geometric Langlands program. The first result is an analogue of the Ramanujan conjecture: any cuspidal D-module on Bun_G is tempered. We actually prove a more…

The paper has two parts, in the first part, we apply the localisation technique to the Rozansky-Witten theory on compact HyperK\"ahler targets. We do so via first reformulating the theory as some supersymmetric sigma-model. We obtain the…

In this paper we provide an explicit construction of star products on U(g)-module algebras by using the Fedosov approach. This construction allows us to give a constructive proof to Drinfel'd theorem and to obtain a concrete formula for…

We formulate a Beilinson-Bernstein type derived equivalence for a quantized enveloping algebra at a root of 1 as a conjecture. It says that there exists a derived equivalence between the category of modules over a quantized enveloping…

We investigate local and global weighted heights a-la Weil for weighted projective spaces via Cartier and Weil divisors and extend the definition of weighted heights on weighted projective spaces from arXiv:1902.06563 to weighted varieties…

We study log D-modules on smooth log pairs and construct a comparison theorem of log de Rham complexes. The proof uses Sabbah's generalized b-functions. As applications, we deduce a log index theorem and a Riemann-Roch type formula for…