arXiv research

We present the complex analytic and principal complex analytic realizability of a link in a 3-manifold $M$ as a tool for understanding the complex structures on the cone $C(M)$.

We deal with smooth real manifolds as well as complex analytic manifolds as well. It is well known that the concept of star product is powerful enough to produce all Poisson structures on real manifolds. According to [BdM] it is not known whether holomorphic star products exist on complex analytic manifolds. The main p…

It is a classical result that any complex analytic Lie supergroup $\mathcal{G}$ is split \cite{kosz}, that is its structure sheaf is isomorphic to the structure sheaf of a certain vector bundle. However, there do exist non-split complex analytic homogeneous supermanifolds. We study the question how to find out whether …

Complex analytic sets' Lipschitz geometry at infinity characterized.

Proves Kähler-Ricci shrinkers are complex analytic varieties.

The article proves a complex analytic inequality for stable Q-sheaves on Kähler varieties.

Given a complex analytic function f on a Whitney stratified complex analytic variety of complex dimension n, whose real part Re(f) is Morse, we prove the existence of a stratified gradient-like vector field for Re(f) such that the unstable set of a critical point p on a stratum S of complex dimension s has real dimensi…

Survey of complex analytic methods in minimal surface theory.

The paper introduces a new complex analytic invariant called the pointed harmonic volume and its relation to the Johnson homomorphism.

We obtain a classification up to isomorphism of complex-analytic supermanifolds with underlying space $\mathbb{CP}^1$ of dimension $1|3$ with retract $(k,k,k)$, where $k\in \mathbb{Z}$. More precisely, we prove that classes of isomorphic complex-analytic supermanifolds of dimension $1|3$ with retract $(k,k,k)$ are in o…

Hopf manifolds can be given lcK structures, shown by constructing a family.

Given a sequence of complete(compact or noncompact) Kähler manifolds $M^n_i$ with bisectional curvature lower bound and noncollapsed volume, we prove that the pointed Gromov-Hausdorff limit is homeomorphic to a normal complex analytic space. The complex analytic structure is the natural "limit" of complex structure of …

Researchers create a new moduli space for Fano manifolds with special geometric properties.

Explains complex analytic invariants of vector fields and foliations.

Study shows indices of 1-forms on G-varieties match, revealing new Milnor number concept.

In this paper, we define a concept of a family of compact holomorphic Poisson manifolds on the basis of Kodaira-Spencer's deformation theory and deduce the integrability condition. We prove an analogue of their `Theorem of existence for complex analytic structures' under some analytic assumption, and establish an analo…

Study projective structures and rational curves to understand Painlevé equations.

Applying a local Gauss-Bonnet formula for closed subanalytic sets to the complex analytic case, we obtain characterizations of the Euler obstruction of a complex analytic germ in terms of the Lipschitz-Killing curvatures and the Chern forms of its regular part. We also prove analogous results for the global Euler obstr…

An important part of the classical theory of real or complex manifolds is the theory of (smooth, real analytic or complex analytic) vector bundles. With any vector bundle over a manifold (M,F) the sheaf of its (smooth, real analytic or complex analytic) sections is associated which is a locally free sheaf of F-modules,…

Grauert constructs complete Kähler metrics on complements of complex analytic sets.

Proves real analyticity on surfaces based on restrictions.

Study families of Lie algebroids on complex spaces, introducing unfoldings.

A model for elliptic cohomology uses quantum field theory.

The period is a classical complex analytic invariant for a compact Riemann surface defined by integration of differential 1-forms. It has a strong relationship with the complex structure of the surface. In this chapter, we review another complex analytic invariant called the harmonic volume. It is a natural extension o…

Develops Bialynicki-Birula and Morse-Bott theory for complex analytic spaces.

We prove that a generic complex deformation of a generalized Kummer variety contains no complex analytic tori.

We classify four-dimensional compact solvmanifolds up to diffeomorphism, while determining which of them have complex analytic structures. In particular, we shall see that a four-dimensional compact solvmanifold S can be written, up to double covering, as G/L where G is a simply connected solvable Lie group and L is a …

The most commonly encountered types of complex analytic G-structures and Cartan geometries cannot have singularities of complex codimension 2 or more.

We provide a characterization for complex analytic curves among two-dimensional minimal graphs in $\mathbb{R}^{4}$ via the Jacobian

In this paper we compute the deformation theory of a special class of algebras, namely of Azumaya algebras on a manifold ($C^{\infty}$ or complex analytic).

Study on opers over complex manifolds of dimension one.

Analyzes log canonical pairs using harmonic integrals and dbar-equation theory.

Two rigidity results for Legendrian singularities in complex-analytic category.

Examines properties of holomorphic fibrations in complex geometry.

Paper proves families of singularities can be topologically trivialized.

LCK metrics extended to spaces with quotient singularities, preserving key properties.

We study the moduli space of CR-projective complex foliated tori. We describe it in terms of isotropic subspaces of Grassmannian and we show that it is a normal complex analytic space.

We obtain a Bernstein type result for entire two dimensional minimal graphs in $\mathbb{R}^{4}$, which extends a previous one due to L. Ni. Moreover, we provide a characterization for complex analytic curves.

We calculate relations on characteristic classes which are obstructions preventing closed Kähler manifolds from carrying holomorphic Cartan geometries. We apply these relations to give global constraints on the phase spaces of complex analytic determined and underdetermined systems of differential equations.

We prove that any (real or complex) analytic horizontally conformal submersion from a three-dimensional conformal manifold M to a two-dimensional conformal manifold N can be, locally, `extended' to a unique harmonic morphism from the heaven space of M to N.

The systems of complex analytic second order ordinary differential equations whose solutions close up to become rational curves (after analytic continuation) are characterized by the vanishing of an explicit differential invariant, and turn out to provide an infinite dimensional family of integrable systems.

We study complex analytic (possibly singular) projective connections on the plane. We characterize some of them in terms of their families of integral curves. We also give a beginning of classification of second order odes polynomial in the first and second derivatives, and with holomorphic coefficients.

Study on moduli spaces of branched projective structures on surfaces.

Generators for the module of vector fields liftable over corank 1 stable complex analytic maps from an n-manifold to an (n+1)-manifold are found. This is applied to the classification of the singularities occuring in generic one-parameter families of maps between these spaces.

Counterexample disproves completeness of model space forcing regularity in infinite-dimensional Lie groups.

We show that a map between complex-analytic manifolds, at least one of which is in the Fujiki class, is a biholomorphism under a natural condition on the second cohomologies. We use this to establish that, with mild restrictions, a certain relation of "domination" introduced by Gromov is in fact a partial order.

Constructs maps from field theories to complexified K-theory and elliptic cohomology.

The paper generalizes SKT and HS properties to arbitrary p and studies their deformation stability.