Related papers: The relative hermitian duality functor

Let G be a connected complex reductive group and let K be a symmetric subgroup of G. We prove a formula for the Drinfeld-Gaitsgory functor for the dg-category of K-equivariant sheaves on the flag manifold of G in terms of the Matsuki…

Here we carefully construct an equivalence between the derived category of coherent sheaves on an elliptic curve and a version of the Fukaya category on its mirror. This is the most accessible case of homological mirror symmetry. We also…

We develop the theory of relative regular holonomic D-modules with a smooth complex manifold S of arbitrary dimension as parameter space, together with their main functorial properties. In particular, we establish in this general setting…

We give an algebraic description of several modules and algebras related to the vector partition function, and we prove that they can be realized as the equivariant K-theory of some manifolds that have a nice combinatorial description. We…

In this short note, we provide an alternative proof of a notable theorem by Narasimhan and Ramanan. The theorem states that the moduli space of $S$-equivalence classes of semistable rank $2$ vector bundles over a curve $X$ of genus $2$ with…

We generalize a result of Orlov and Van den Bergh on the representability of a cohomological functor from the bounded derived category of a smooth projective variety over a field to the category of L-modules, to the case where L is a field…

The paper studies quadratic and Koszul duality for modules over positively graded categories. Typical examples are modules over a path algebra, which is graded by the path length, of a not necessarily finite quiver with relations. We…

Let $R$ be an associative ring with unit. Given an $R$-module $M$, we can associate the following covariant functor from the category of $R$-algebras to the category of abelian groups: $S\mapsto M\otimes_R S$. With the corresponding notion…

We investigate differential geometric aspects of moduli spaces parametrizing solutions of coupled vortex equations over a compact Kaehler manifold X. These solutions are known to be related to polystable triples via a Kobayashi-Hitchin type…

We introduce a notion of Homological Projective Duality for smooth algebraic varieties in dual projective spaces, a homological extension of the classical projective duality. If algebraic varieties $X$ and $Y$ in dual projective spaces are…

The paper is devoted to the comparison of the Fukaya category (it is responcible for the A-side of mirror symmetry) with the category of holonomic modules over the quantized algebra of functions on the same symplectic manifold. We…

We extend the relation between quasi-modular forms and modular forms to a wider class of functions. We then relate both forms to vector-valued modular forms with symmetric power representations, and prove a general structure theorem for…

The probability content of a convex polyhedron with a multivariate normal distribution can be regarded as a real analytic function. We give a system of linear partial differential equations with polynomial coefficients for the function and…

Based on the usual Fedosov construction of star products for a symplectic manifold M we give a simple geometric construction of a bimodule deformation for the sections of a vector bundle over M starting with a symplectic connection on M and…

We discuss homological mirror symmetry of Fermat polynomials in terms of derived Morita equivalence between derived categories of coherent sheaves and Fukaya-Seidel categories (a.k.a. perfect derived categories of directed Fukaya…

We study the derived category of a complete intersection X of bilinear divisors in the orbifold Sym^2 P(V). Our results are in the spirit of Kuznetsov's theory of homological projective duality, and we describe a homological projective…

Let $h$ be a connective homology theory. We construct a functorial relative plus construction as a Bousfield localization functor in the category of maps of spaces. It allows us to associate to a pair $(X, H)$ consisting of a connected…

For a small category A, we prove that the homotopy colimit functor from the category of simplicial diagrams on A to the category of simplicial sets over the nerve of A establishes a left Quillen equivalence between the projective (or Reedy)…

A local classification of the Hermitian manifolds with flat associated connection is given. Hermitian manifolds admitting locally a conformal metric with flat associated connection are characterized by a curvature identity. Locally…

The aim of this note is threefold. The first is to obtain a simple characterization of relative constructible sheaves when the parameter space is projective. The second is to study the relative Fourier-Mukai for relative constructible…