Related papers: Fourier-Mukai transform for fine compactified Prym…
We construct a Poincar\'e sheaf on the compactified Prym variety associated with an \'etale double cover of integral curves with planar singularities, and prove that the associated Fourier-Mukai transform is an autoequivalence of its…
Given a Fourier-Mukai transform $\Phi$ between the bounded derived categories of two smooth projective curves, we verifiy that the induced map between the Jacobian varieties preserves the principal polarization if and only if $\Phi$ is an…
Let X be an abelian scheme over a scheme B. The Fourier--Mukai transform gives an equivalence between the derived category of X and the derived category of the dual abelian scheme. We partially extend this to certain schemes X over B (which…
To every singular reduced projective curve X one can associate, following E. Esteves, many fine compactified Jacobians, depending on the choice of a polarization on X, each of which yields a modular compactification of a disjoint union of…
We construct a Fourier--Mukai transform for smooth complex vector bundles $E$ over a torus bundle $\pi:M \to B,$ the vector bundles being endowed with various structures of increasing complexity. At a minimum, we consider vector bundles $E$…
For a given Fourier-Mukai equivalence of bounded derived categories of coherent sheaves on smooth quasi-projective varieties, we construct Fourier-Mukai equivalences of derived factorization categories of gauged Landau-Ginzburg (LG) models.…
The paper sets out a generalized framework for Fourier-Mukai transforms and illustrates their use via vector bundle transforms. A Fourier-Mukai transform is, roughly, an isomorphism of derived categories of (sheaves) on smooth varieties X…
To every reduced (projective) curve X with planar singularities one can associate many fine compactified Jacobians, depending on the choice of a polarization on X, which are birational (possibly non-isomorphic) Calabi-Yau projective…
We study Fourier-Mukai transforms for smooth projective varieties whose canonical bundles have finite order, and relate them to equivariant transforms on certain finite covering spaces. Our results lead to new equivalences of derived…
We apply the methods of C{\u{a}}ld{\u{a}}raru to construct a twisted Fourier-Mukai transform between a pair of holomorphic symplectic four-folds. More precisely, we obtain an equivalence between the derived category of coherent sheaves on a…
We study Arinkin's Poincar\'e sheaf $\mathcal{P}_C$ on the singular locus of $\overline{\mathsf{Jac}}_C$, the compactified Jacobian of rank one torsion-free sheaves on an integral nodal projective curve $C$. Each stratum of the singular…
We study the interaction between Fourier-Mukai transforms and perverse filtrations for a certain class of dualizable abelian fibrations. Multiplicativity of the perverse filtration and the "Perverse $\supset$ Chern" phenomenon for these…
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 study a Fourier-Mukai kernel associated to a GIT wall-crossing for arbitrarily singular (not necessarily reduced or irreducible) affine varieties over any field. This kernel is closely related to a derived fiber product diagram for the…
Let C be an integral projective curve with planar singularities. Consider its Jacobian J and the compactified Jacobian J'. We construct a flat family P of Cohen-Macaulay sheaves on J' parametrized by J'; over J, the family P is the Poincare…
We use twisted Fourier-Mukai transforms to study the relation between an abelian fibration on a holomorphic symplectic manifold and its dual fibration. Our reasoning leads to an equivalence between the derived category of coherent sheaves…
Given a polarized tropical affine torus, we show that the fibered Lagrangian cobordism group of the corresponding symplectic manifold admits a natural geometric filtration of finite length. This contrasts with results of Sheridan-Smith in…
In this paper we construct the Poincare line bundle for the stack of Higgs bundles on smooth projective curves and show that it induces a fully-faithful Fourier-Mukai transform on the category of quasi-coherent sheaves.
We study relative Fourier-Mukai transforms on genus one fibrations with section, allowing explicitly the total space of the fibration to be singular and non-projective. Grothendieck duality is used to prove a skew-commutativity relation…
In this paper I construct a geometric transformation for generalized 1-motives which extends the Fourier-Mukai transformation for O-Modules on abelian varieties, the geometric Fourier transformation for D-Modules on vector spaces and the…