相关论文: Buchsbaum-Rim sheaves and their multiple sections

A great number of theoretical results are known about log Gromov-Witten invariants, but few calculations are worked out. In this paper we restrict to surfaces and to genus 0 stable log maps of maximal tangency. We ask how various natural…

Let $R$ be a domain that is a complete local $\mathbb{k}$ algebra in dimension one. In an effort to address the Berger's conjecture, a crucial invariant reduced type $s(R)$ was introduced by Huneke et. al. In this article, we study this…

We give an explicit description of toric sheaves on the weighted projective plane $\mathbb{P}(a,b,c)$ viewed as a toric Deligne-Mumford stack. The integers $(a,b,c)$ are not necessarily chosen coprime or mutually coprime allowing for gerbe…

We construct explicit tableau-level maps between indecomposable projective modules for the type A 0-Hecke algebra that assemble into canonical split short exact sequences lifting the basic ribbon product rule in NSym via concatenation and…

In math.RT/0304173 the derived category of the principal block in modules over the Lusztig quantum algebra at a root of unity is related to the derived category of equivariant coherent sheaves on the Springer resolution. In the present…

We develop and collect techniques for determining Hochschild cohomology of skew group algebras S(V)#G and apply our results to graded Hecke algebras. We discuss the explicit computation of certain types of invariants under centralizer…

We study the cohomology theory of sheaf complexes for open embeddings of topological spaces and related subjects. The theory is situated in the intersection of the general Cech theory and the theory of derived categories. That is to say, on…

A primitive multiple scheme is a Cohen-Macaulay scheme $Y$ such that the associated reduced scheme $X=Y_{red}$ is smooth, irreducible, and that $Y$ can be locally embedded in a smooth variety of dimension $\dim(X)+1$. If $I_X$ is the ideal…

Let $C$ be a completely algebraic closed non-archimedean field over $\mathbb{Q}_p$ and $\alpha,r$ be two positive integers. Denote by $B_\alpha$ the ring $\mathbb{B}_{\mathrm{dR}}^+(C)/(\ker\theta)^\alpha$. This paper first constructs a…

We study the spectrum of rank $2$ torsion free sheaves on $\mathbb{P}^3$ with aim of producing examples of distinct irreducible components of the moduli space with the same spetrcum answering the question presented by Rao for the case of…

Let $M$ be a smooth algebraic variety of dimension $2(p+q)$ with an algebraic symplectic form and a compatible deformation quantization $\mathcal{O}_h$ of the structure sheaf. Consider a smooth coisotropic subvariety $j: Y \to M$ of…

The Dolbeault resolution of the sheaf of holomorphic vector fields $Lie$ on a complex manifold $M$ relates $Lie$ to a sheaf of differential graded Lie algebras, known as the Fr\"olicher-Nijenhuis algebra $g$. We establish - following B. L.…

Quantum sheaf cohomology is a deformation of the cohomology ring of a sheaf. In recent years, this subject had an impetuous development in connection with the $(0; 2)$ non-linear sigma model from super-strings theory. The basic piece in…

We give an exact algorithm to calculate (under some GKM-restriction) the matrix describing the embedding $\B(\s)_x\subset\B(\s)^x$, where the first module is the costalk and the second one is the stalk at $x$ of a Bott-Samelson module…

An important part of the classical theory of real or complex manifolds is the theory of (smooth, real analytic or complex analytic) vector bundles. With any vector bundle over a manifold (M,F) the sheaf of its (smooth, real analytic or…

Let X be a quasi-compact scheme, equipped with an open covering by affine schemes. A quasi-coherent sheaf on X gives rise, by taking sections over the covering sets, to a diagram of modules over the various coordinate rings. The resulting…

In this brief note, we investigate graded functions of linear stacks in derived geometry. In particular, we show that under mild assumptions, we can recover a quasi-coherent sheaf on a derived stack from the data of the…

Let S be a smooth projective algebraic surface. Generalizing results of Nakajima and Grojnowski, we construct (under some assumptions) an action of the oscillator algebra associated to the cohomology of S, on the cohomology of the moduli…

The Gieseker-Uhlenbeck morphism maps the Gieseker moduli space of stable rank-2 sheaves on a smooth projective surface to the Uhlenbeck compactification, and is a generalization of the Hilbert-Chow morphism for Hilbert schemes of points.…

We study sheaves of Lie-Rinehart algebras over locally ringed spaces. We introduce morphisms and comorphisms of such sheaves and prove factorization theorems for each kind of morphism. Using this notion of morphism, we obtain (higher)…