Related papers: A simpler kernel for stratified Mukai flops
By interpreting the product of the Principal Component Analysis, that is the covariance matrix, as a sequence of nested subspaces naturally coming with weights according to the level of approximation they provide, we are able to embed all…
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…
We give a self-contained and simplified proof of Mukai's classification of prime Fano threefolds of index 1 and genus $g \ge 6$ with at most Gorenstein factorial terminal singularities, and of its extension to higher-dimension.
We compute a large number of moduli spaces of stable bundles on a general algebraic elliptic surface using a new class of Fourier-Mukai type transforms.
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 introduce a class of flops between projective varieties modelled on direct sums of universal subbundles of Grassmannians. We study basic properties of these flops.
We study the Fourier--Mukai numbers of rational elliptic surfaces. As its application, we give an example of a pair of minimal 3-folds with Kodaira dimensions 1, $h^1(\mc O)=h^2(\mc O)=0$ such that they are mutually derived equivalent,…
In a recent preprint, Y. Namikawa proposed a conjecture on Q-factorial terminalizations and their birational geometry of nilpotent orbits. He proved his conjecture for classical simple Lie algebras. In this note, we prove his conjecture for…
We examine an application of the kernel-based interpolation to numerical solutions for Zakai equations in nonlinear filtering, and aim to prove its rigorous convergence. To this end, we find the class of kernels and the structure of…
We present a technique for computing explicit, concrete formulas for the weighted Bergman kernel on a planar domain with weight the modulus squared of a meromorphic function in the case that the meromorphic function has a finite number of…
In this note, we shall prove that two smooth projective varieties of dim 2n connected by a Mukai flop have equivalent bounded derived categories. More precisely, let $\phi : X - - \to X^+$ be a Mukai flop with centers $Y \subset X$ and $Y^+…
Coherent, continuous spatial representations are critical for synthesizing physical and perceptual phenomena into a single representational space. Radial basis kernels provide a path forward for this type of distributed representation. In…
Consider a finite covering $\beta : C \to X$ of a smooth projective curve $X$ by a reduced, projective, planar curve $C$. Associated to two general polarizations on $C$, $q$ and $q'$, one can construct the corresponding compactified Prym…
We address the uniqueness problem of dg-lifts of exact functors between triangulated categories, and its relationship with the uniqueness problem of Fourier-Mukai kernels. We prove a positive result under a vanishing hypothesis on the…
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 give a condition for an exact functor between triangulated categories to be an equivalence. Applications to Fourier-Mukai transforms are discussed. In particular, we obtain a large number of such transforms for K3 surfaces.
Given a pair of derived-equivalent Calabi--Yau manifolds of dimension more than two, we prove that the derived equivalence can be extended to general fibers of versal deformations. As an application, we give a new proof of the…
The Fourier-Mukai transform is lifted to the derived category of sheaves with connection on abelian varieties. The case of flat connections (D-modules) is discussed in detail.
Associated to a Mukai flop X ---> X' is on the one hand a sequence of equivalences D(X) -> D(X'), due to Kawamata and Namikawa, and on the other hand a sequence of autoequivalences of D(X), due to Huybrechts and Thomas. We work out a…
We survey and investigate some computational aspects of the Fourier-Mukai transform.