Related papers: Good formal structure for meromorphic flat connect…
Polyhedral surfaces are fundamental objects in architectural geometry and industrial design. Whereas closeness of a given mesh to a smooth reference surface and its suitability for numerical simulations were already studied extensively, the…
We show that for a given holomorphic noncharacteristic surface S in two-dimensional complex space, and a given holomorphic function on S, there exists a unique meromorphic solution of Burgers' equation which blows up on S. This proves the…
Explicit representations of complex structures on closed manifolds are valuable, but relatively rare in the literature. Using isoparametric theory, we construct complex structures on isoparametric hypersurfaces with $g=4, m=1$ in the unit…
The relationship between comodules of a coring and flat connections is reviewed. In particular we specialise to corings which are built on a tensor product of algebra and a coalgebra. Such corings are in one-to-one correspondence with…
We investigate when a meromorphic connection on a smooth rigid analytic variety $X$ gives rise to a coadmissible $\mathcal{D}_X$-cap-module, and show that this is always the case when the roots of the corresponding $b$-functions are all of…
We develop some foundations for the theory of formal derived algebraic geometry, which parallel the theory of formal spectral algebraic geometry by Jacob Lurie. For this, we establish a close connection between algebro-geometric objects in…
We introduce a new technique that is used to show that the complex projective plane blown up at 6, 7, or 8 points has infinitely many distinct smooth structures. None of these smooth structures admit smoothly embedded spheres with…
We prove the existence of normal forms for some local real-analytic Levi-flat hypersurfaces with an isolated line singularity. We also give sufficient conditions for that a Levi-flat hypersurface with a complex line as singularity to be a…
We provide a simple condition on rational cohomology for the total space of a pullback fibration over a connected sum to have the rational homotopy type of a connected sum, after looping. This takes inspiration from recent work of Jeffrey…
Necessary and sufficient conditions for some deformation algebras to provide formal Frobenius structures are given. Also, examples of formal Frobenius structures with fundamental tensor that is not of the deformation type and examples of…
Examples of nonformal simply connected symplectic manifolds are constructed.
We prove the nonequivariant coherent-constructible correspondence conjectured by Fang-Liu-Treumann-Zaslow in the case of toric surfaces. Our proof is based on describing a semi-orthogonal decomposition of the constructible side under toric…
We study the holomorphic equivalence problem for finite type hypersurfaces in $\mathbb C^2$. We discover a geometric condition, which is sufficient for the existence of a natural convergent normal form for a finite type hypersurface. We…
In this paper we prove that every open Riemann surface properly embeds in the Special Linear group $SL_2(\mathbb{C})$ as a holomorphic Legendrian curve, where $SL_2(\mathbb{C})$ is endowed with its standard contact structure. As a…
In this note we describe conditions under which the algebras for a monad on a presheaf category equipped with some additional structure are fibrant objects in a model structure. We also prove that when these conditions are satisfied the…
In this paper we study the topology of the space $\I_\omega$ of complex structures compatible with a fixed symplectic form $\omega$, using the framework of Donaldson. By comparing our analysis of the space $\I_\omega$ with results of McDuff…
The complex structure of a surface generated by the two-dimensional dynamical triangulation(DT) is determined by measuring the resistivity of the surface. It is found that surfaces coupled to matter fields have well-defined complex…
We give a sufficient condition under which the fundamental group of a reglued graph of surfaces is hyperbolic. A reglued graph of surfaces is constructed by cutting a fixed graph of surfaces along the edge surfaces, then regluing by…
The well known $g$-conjecture for homology spheres follows from the stronger conjecture that the face ring over the reals of a homology sphere, modulo a linear system of parameters, admits the strong-Lefschetz property. We prove that the…
Using a recent description of the geometric stability manifold, we show the geometric stability manifold associated to any smooth projective complex surface is contractible. We then use this result to demonstrate infinitely many new…