Related papers: Fourier-Mukai transforms and the decomposition the…

In this paper, we consider the preservation of stability by using the notion of Twisted stability. As applications, (1) we show that moduli spaces of vector bundles on K3 and abelian surfaces are irreducible, (2) we compute Hodge…

This paper discusses the overlap of the Hori-Vafa formulation of mirror symmetry with some other constructions. We focus on compact Calabi-Yau hypersurfaces \mathcal{M}_G = {G = 0} in weighted complex projective spaces. The Hori-Vafa…

Let (X,\Omega) be a closed polarized complex manifold, g be an extremal metric on X that represents the K\"ahler class \Omega, and G be a compact connected subgroup of the isometry group Isom(X,g). Assume that the Futaki invariant relative…

We survey and investigate some computational aspects of the Fourier-Mukai transform.

We construct a new infinite series of irreducible components of the Gieseker-Maruyama moduli scheme $\mathcal{M}(k), ~ k \geq 3$ of coherent semistable rank 2 sheaves with Chern classes $c_1=0,~ c_2=k,~ c_3=0$ on $\mathbb{P}^3$ whose…

We associate a family of ideal sheaves to any Q-effective divisor on a complex manifold, called higher multiplier ideals, using the theory of mixed Hodge modules and V-filtrations. This family is indexed by two parameters, an integer…

Wedge product on deRham complex of a Riemannian manifold $M$ can be pulled back to $H^*(M)$ via explicit homotopy, constructed using Green's operator, to give higher product structures. We prove Fukaya's conjecture which suggests that…

By using a Fourier-Mukai transform for sheaves on K3 surfaces we show that for a wide class of K3 surfaces $X$ the punctual Hilbert schemes $\Hilb^n(X)$ can be identified, for all $n\geq 1$, with moduli spaces of Gieseker stable vector…

Let $X$ be a closed subscheme embedded in a scheme $W$ smooth over a field ${\bf k}$ of characteristic zero, and let ${\mathcal I}(X)$ be the sheaf of ideals defining $X$. Assume that the set of regular points of $X$ is dense in $X$. We…

In this paper, we establish a logarithmic vanishing theorem on weakly pseudoconvex K\"ahler manifolds, where the divisor may have infinitely many irreducible components. This result serves as a generalization of Norimatsu's findings on…

In this paper we introduce the Fourier-Mukai transform for Lawson homology of abelian varieties and prove an inversion theorem for the Lawson homology as well as the morphic cohomology of abelian varieties. As applications, we obtain the…

We develop a unified approach for establishing rates of decay for the Fourier transform of a wide class of dynamically defined measures. Among the key features of the method is the systematic use of the $L^2$-flattening theorem obtained in…

Suppose we are given complex manifolds $X$ and $Y$ together with substacks $\mathcal{S}$ and $\mathcal{S}'$ of modules over algebras of formal deformation $\mathcal{A}$ on $X$ and $\mathcal{A}'$ on $Y$, respectively. Suppose also we are…

Let $X$, $Y$ be smooth projective varieties over $\mathbf{C}$. Let $K$ be a bounded complex of coherent sheaves on $X\times Y$ and let $\Phi_K \colon \mathsf{D}^b_{\mathsf{Coh}}(X) \to \mathsf{D}^b_{\mathsf{Coh}}(Y)$ be the resulting…

This paper studies deformations and birational maps between singular moduli spaces of semistable sheaves with 2-divisible Mukai vectors on K3 surfaces. It is showed that under certain conditions, two such moduli spaces of the same dimension…

The construction of a satisfactory dg category of logarithmic coherent sheaves remains a central open problem in logarithmic geometry. In this paper, we propose an alternative correspondence-theoretic approach based on logarithmic…

We prove that the kernels of Fourier-Mukai functors are not unique in general. On the other hand we show that the cohomology sheaves of those kernels are unique. We also discuss several properties of the functor sending an object in the…

We prove that a torsion-free sheaf $\mathcal F$ endowed with a singular hermitian metric with semi-positive curvature and satisfying the minimal extension property admits a direct-sum decomposition $\mathcal F \simeq \mathcal U \oplus…

Over an arbitrary compact complex space or an arbitrary germ of complex space $X$, we provide fine resolutions of pure Hodge modules with strict supports $IC_X(\mathbb{V})$ via differential forms with locally $L^2$ boundary conditions. When…

Motivated by classical Alexander invariants of affine hypersurface complements, we endow certain finite dimensional quotients of the homology of abelian covers of complex algebraic varieties with a canonical and functorial mixed Hodge…