Related papers: Sectorial covers over fanifolds
We introduce and study the category of Hodge microsheaves which is a Hodge-version of the category of microsheaves for a certain class of holomorphic exact symplectic manifolds. We then study Hodge-theoretic version of wrapped sheaves and…
We survey some recent results concerning the so called Categorical Torelli problem. This is to say how one can reconstruct a smooth projective variety up to isomorphism, by using the homological properties of special admissible…
Let $k$ be a commutative Noetherian ring and $\underline{\mathscr{C}}$ be a locally finite $k$-linear category equipped with a self-embedding functor of degree 1. We show under a moderate condition that finitely generated torsion…
We identify the twisted sectors of a compact simplicial toric variety. We do the same for a generic nondegenerate Calabi-Yau hypersurface of an $n$-dimensional simplicial Fano toric variety and then explicitly compute $h^{1,1}_{orb}$ and…
Inspired by the homological mirror symmetry conjecture of Kontsevich, we construct new classes of automorphisms of the bounded derived category of coherent sheaves on a smooth Calabi-Yau variety.
We prove a homological mirror symmetry result for maximally degenerating families of hypersurfaces in $(\mathbb{C}^*)^n$ (B-model) and their mirror toric Landau-Ginzburg A-models. The main technical ingredient of our construction is a…
We present a novel proof technique to construct the Gelfand-Fuks spectral sequence for diagonal Chevalley-Eilenberg cohomology of vector fields on a smooth manifold, performing a local-to-global analysis through a notion of generalized good…
We consider differential forms associated to Campana's geometric orbifolds from a new perspective, namely, as a qfh-sheaf on the variety underlying the geometric orbifold. This approach avoids having to choose a covering of the underlying…
We introduce a type of surgery decomposition of Weinstein manifolds we call simplicial decompositions. The main result of this paper is that the Chekanov-Eliashberg dg-algebra of the attaching spheres of a Weinstein manifold satisfies a…
We use symplectic cohomology to study the non-uniqueness of symplectic structures on the smooth manifolds underlying affine varieties. Starting with a Lefschetz fibration on such a variety and a finite set of primes, the main new tool is a…
A Stein covering of a complex manifold may be used to realise its analytic cohomology in accordance with the Cech theory. If, however, the Stein covering is parameterised by a smooth manifold rather than just a discrete set, then we…
We consider the subspace of the homology of a covering space spanned by lifts of simple closed curves. Our main result is the existence of unbranched covers of surfaces where this is a proper subspace. More generally, for a fixed finite…
We show that any star-shaped convex hypersurface with constant Weingarten curvature in the deSitter-Schwarzschild manifold is a sphere of symmetry. Moreover, we study an isoperimetric problem for bounded domains in the doubled Schwarzschild…
We prove the quasimodularity of generating functions for counting pillowcase covers, with and without Siegel-Veech weight. Similar to prior work on torus covers, the proof is based on analyzing decompositions of half-translation surfaces…
In this paper we investigate the functoriality properties of map-graded Hochschild complexes. We show that the category MAP of map-graded categories is naturally a stack over the category of small categories endowed with a certain…
Recent investigation of locality problem for higher-spin fields led to a vertex reconstruction procedure that involved elements of contraction of the original Vasiliev interaction algebra. Inspired by these results we propose the…
Helmut Hofer introduced in '93 a novel technique based on holomorphic curves to prove the Weinstein conjecture. Among the cases where these methods apply are all contact 3--manifolds $(M,\xi)$ with $\pi_2(M) \ne 0$. We modify Hofer's…
On a Weinstein manifold, we define a constructible co/sheaf of categories on the skeleton. The construction works with arbitrary coefficients, and depends only on the homotopy class of a section of the Lagrangian Grassmannian of the stable…
We prove that the wrapped Fukaya category of a punctured sphere ($S^2$ with an arbitrary number of points removed) is equivalent to the triangulated category of singularities of a mirror Landau-Ginzburg model, proving one side of the…
It is well known that isoperimetric regions in a smooth compact $(n+1)$-manifold are smooth, up to a closed set of codimension at most $6$. In this note, we first construct an $8$-dimensional compact smooth manifold whose unique…