Related papers: Fourier-Mukai transforms and the decomposition the…
This is the first in a series of papers that deals with duality statements such as Mukai-duality (T-duality, from algebraic geometry) and the Baum-Connes conjecture (from operator $K$-theory). These dualities are expressed in terms of…
We define a Fourier-Mukai transform for a triple consisting of two holomorphic vector bundles over an elliptic curve and a homomorphism between them. We prove that in some cases the transform preserves the natural stability condition for a…
Given a non-singular variety with a K3 fibration f : X --> S we construct dual fibrations Y --> S by replacing each fibre X_s of f by a two-dimensional moduli space of stable sheaves on X_s. In certain cases we prove that the resulting…
We exhibit a transformation taking special Lagrangian submanifolds of a Calabi-Yau together with local systems to vector bundles over the mirror manifold with connections obeying deformed Hermitian-Yang-Mills equations. That is, the…
We show that any orientation preserving Hodge isometry between the Hodge structures of two K3 surfaces X and X' twisted by Brauer classes $\alpha$ resp. $\alpha'$ can be lifted to a Fourier-Mukai equivalence between the derived categories…
These are the lecture notes based on earlier papers with some additional new results. New and simple proofs are given for local freeness theorem and the semipositivity theorem. A decomposition theorem for higher direct images of dualizing…
We prove that a coherent DQ-kernel induces an equivalence between the derived categories of DQ-modules with coherent cohomology if and only if the graded commutative kernel associated to it induces an equivalence between the derived…
We propose a slightly modified definition for the Fourier-Mukai transform (on abelian varieties) that makes it much easier to remember various formulas. As an application, we give relatively short proofs for two important theorems: the…
We give a formalism of arithmetic mixed sheaves including the case of arithmetic mixed Hodge structures, and show the nonvanishing of certain higher extension groups, and also the nontriviality of the second Abel-Jacobi map for zero cycles…
We construct the moduli of twisted sheaves on a projective variety. Then we generalize known results on the moduli space of usual sheaves on a K3 surface to the twisted case. Thus we consider the non-emptyness, the deformation type and the…
We introduce new enhancements for the bounded derived category $D^b(Coh(X))$ of coherent sheaves on a suitable scheme $X$ and for its subcategory $Perf(X)$ of perfect complexes. They are used for translating Fourier-Mukai functors to…
On a Weierstra{\ss} elliptic surface $X$, we define a `limit' of Bridgeland stability conditions, denoted $Z^l$-stability, by varying the polarisation in the definition of Bridgeland stability along a curve in the ample cone of $X$. We show…
Let $X$ be a smooth projective variety. We study a relationship between the derived category of $X$ and that of a canonical divisor. As an application, we will study Fourier-Mukai transforms when $\kappa (X)=dim X-1$.
We consider a relative Fourier-Mukai transform defined on elliptic fibrations over an arbitrary normal base scheme. This is used to construct relative Atiyah sheaves and generalize Atiyah's and Tu's results about semistable sheaves over…
We study a system of equations on a compact complex manifold, that couples the scalar curvature of a Kaehler metric with a spectral function of a first-order deformation of the complex structure. The system comes from an…
We prove that a standard realization of the direct image complex via the so-called Douady-Barlet morphism associated with a smooth complex analytic surface admits a natural decomposition in the form of an injective quasi-isomorphism of…
We determine the group of all Fourier-Mukai type autoequivalences of Kuznetsov components of smooth complex cubic threefolds, and provide yet another proof for the Fourier-Mukai version of categorical Torelli theorem for smooth complex…
Let $X$ be a complex manifold, and let $Y$ and $D$ be two reduced simple-normal-crossing (snc) divisors on $X$ with no common irreducible components. Given a proper locally K\"ahler morphism $\pi \colon X \to \Delta$ from $X$ to a complex…
Cohesive modules give a dg-enhancement of the bounded derived category of coherent sheaves on a complex manifold via superconnections. In this paper we discuss the deformation theory of cohesive modules on compact complex manifolds. This…
In a previous article (J. Algebra 367 (2012), 142-165) we established axiomatic parametrised Cohen-Macaulay approximation which in particular was applied to pairs consisting of a finite type flat family of Cohen-Macaulay rings and modules.…