arXiv research

Introduces new holomorphic contact structures and proves unobstructedness theorems.

Homotopy operators help describe structures in equivariant deformation problems.

We determine obstructedness or unobstructedness of (holomorphic) Poisson deformations of ruled surfaces over an elliptic curve.

We give a new characterization of generalized Kähler structures in terms of their corresponding complex Dirac structures. We then give an alternative proof of Hitchin's partial unobstructedness for holomorphic Poisson structures. Our main application is to show that there is a corresponding unobstructedness result for …

Extends deformation theory to higher-page analogues of manifolds.

The paper examines Kodaira dimensions of specific complex 4-manifolds with torsion first Chern class.

We give a new Tian-Todorov lemma on deformations of CR-structures and use it to reprove the deformation unobstructedness of normal compact strongly pseudoconvex CR-manifold under the assumption of $d'd''$-lemma, more faithfully following Tian-Todorov's approach.

An unobstructedness theorem is proved for deformations of compact holomorphic Poisson manifolds and applied to a class of examples. These include certain rational surfaces and Hilbert schemes of points on Poisson surfaces. We study in particular the Hilbert schemes of the projective plane and show that a generic deform…

Let $X$ be a normal compact Kähler space with klt singularities and torsion canonical bundle. We show that $X$ admits arbitrarily small deformations that are projective varieties if its locally trivial deformation space is smooth. We then prove that this unobstructedness assumption holds in at least three cases: if $X$…

In \cite{Goto}, Ryushi Goto has constructed the deformation space for a manifold equipped with a collection of closed differential forms and showed that in some important cases (Calabi-Yau, $G_2$- and $Spin(7)$-structures) this deformation space is smooth. This result unifies the classical Bogomolov-Tian-Todorov and Jo…

Analyzes complex structure deformations using cohomology contraction methods.

Paper proves all Lagrangians unobstructed if one is, using non-archimedean analytic structure.

The article provides conditions for unobstructedness of ASD manifolds.

We investigate the formal deformation theory of (rank 1) branes on generalized complex (GC) manifolds. This generalizes, for example, the deformation theory of a complex submanifold in a fixed complex manifold. For each GC brane $\mathcal{B}$ on a GC manifold $(X,\mathbb{J})$, we construct a formal (pointed) groupoid $…

A stable generalized complex structure is one that is generically symplectic but degenerates along a real codimension two submanifold, where it defines a generalized Calabi-Yau structure. We introduce a Lie algebroid which allows us to view such structures as symplectic forms. This allows us to construct new examples o…

Study on the existence of Dirac complements for Dirac structures.

We construct a simply connected minimal complex surface of general type with $p_g=0$ and $K^2=2$ which has an involution such that the minimal resolution of the quotient by the involution is a simply connected minimal complex surface of general type with $p_g=0$ and $K^2=1$. In order to construct the example, we combin…

We present a new method to solve certain $\bar{\partial}$-equations for logarithmic differential forms by using harmonic integral theory for currents on Kahler manifolds. The result can be considered as a $\bar{\partial}$-lemma for logarithmic forms. As applications, we generalize the result of Deligne about closedness…

Study properties of holomorphic $p$-contact manifolds, including non-Kähler hyperbolicity and deformations.

The paper generalizes hyperkahler metrics near Lagrangian submanifolds.

The paper extends deformation theory to Calabi-Yau varieties with isolated log canonical singularities.

Given a compact symplectic toric manifold $(M,ω, \mathbb{T})$, we identify a class $DGK_ω^{\mathbb{T}}(M)$ of $\mathbb{T}$-invariant generalized Kähler structures for which a generalisation the Abreu-Guillemin theory of toric Kähler metrics holds. Specifically, elements of $DGK_ω^{\mathbb{T}}(M)$ are characterized by t…

New non-Kähler 3-folds constructed via log conifold transitions.

In this paper, we 'construct' a 2-functor from the unobstructed immersed Weinstein category to the category of all filtered $A_{\infty}$ categories. We consider arbitrary (compact) symplectic manifolds and its arbitrary (relatively spin) immersed Lagrangian submanifolds. The filtered $A_{\infty}$ category associated to…