Related papers: Stability of Abelian Complex Structures

In this paper, we are concerned with studying the existence of invariant complex manifolds of two-dimensional holomorphic systems. From the geometric singular perturbation theory we know that if a slow-fast system has associated a normally…

Let X be an irreducible symplectic manifold and Def(X) the Kuranishi space. Assume that X admits a Lagrangian fibration. We prove that X can be deformed preserving a Lagrangian fibration. More precisely, there exists a smooth hypersurface H…

In our previous works on deformation limits of projective and Moishezon manifolds, we introduced and made crucial use of the notion of strongly Gauduchon metrics as a reinforcement of the earlier notion of Gauduchon metrics. Using direct…

In this paper we explicitly show that the various noncompact abelian orbifolds are realized as special limits of parameters in type II (NSNS) Melvin background and its higher dimensional generalizations. As a result the supersymmetric ALE…

We consider Poisson superalgebras with constant nondegenerate bracket realized on the smooth Grassmann-valued functions with compact supports in R^{2n}. The deformations with even and odd deformation parameters of these superalgebras are…

We discuss deformations of orbifold singularities on tilted tori in the context of Type IIA orientifold model building with D6-branes on special Lagrangian cycles. Starting from $T^6/(\mathbb{Z}_2 \times \mathbb{Z}_2)$, we mod out an…

The aim of this article is to study the existence of invariant SKT structures on nilmanifolds. More precisely, we give a negative answer to the question of whether there exist a $k$-step ($k>2$) complex nilmanifold admitting an invariant…

We study bi-Lagrangian structures (a symplectic form with a pair of complementary Lagrangian foliations, also known as para-K\"ahler or K\"unneth structures) on nilmanifolds of dimension less than or equal to 6. In particular, building on…

We study nonanticommutative deformations of N=2 two-dimensional Euclidean sigma models. We find that these theories are described by simple deformations of Zumino's Lagrangian and the holomorphic superpotential. Geometrically, this…

In this note we consider low dimensional metric Leibniz algebras with an invariant inner product over the complex numbers up to five dimension. We study their deformations, and give explicit formulas for the cocycles and deformations. We…

We construct universal local deformations (Kuranishi families) for pairs consisting of a compact complex curve and a meromorphic 1-form. Each pair is assumed to be locally planar, a condition which in particular forces the periods of the…

We show that the existence of a left-invariant pluriclosed Hermitian metric on a unimodular Lie group with a left-invariant abelian complex structure forces the group to be $2$-step nilpotent. Moreover, we prove that the pluriclosed flow…

The Kuranishi family of the Iwasawa manifold give rise naturally to a family of (deformed) double complexes. By using the structure theorem of double complexes due to Stelzig and Qi-Khovanov, we show there are exactly $3$ isomorphism types…

We prove that the Gorenstein locus of the Hilbert scheme of points on $\mathbb A^n$ is non-reduced for $n\geq 12$; we construct examples of non-reduced points that come from apolar algebras of the sum of general cubics. As a corollary, we…

It is conjectured that the Dolbeault cohomology of a complex nilmanifold $X$ is computed by left-invariant forms. We prove this under the assumption that $X$ is suitably foliated in toroidal groups and deduce that the conjecture holds in…

We study almost complex structures with lower bounds on the rank of the Nijenhuis tensor. Namely, we show that they satisfy an $h$-principle. As a consequence, all parallelizable manifolds and all manifolds of dimension $2n\geq 10$…

We consider stable manifolds of a holomorphic diffeomorphism of a complex manifold. Using a conjugation of the dynamics to a (non-stationary) polynomial normal form, we show that typical stable manifolds are biholomorphic to complex…

Let $(M,J)$ be a complex manifold of complex dimension $n$. A $p$-K\"ahler structure on $(M,J)$ is a real, closed $(p,p)$-transverse form. In this paper, we address the conjecture of L. Alessandrini and G. Bassanelli on $(n-2)$-K\"ahler…

Using examples of compact complex 3-manifolds which arise as twistor spaces, we show that the class of compact complex manifolds bimeromorphic to K\"ahler manifolds is not stable under small deformations of complex structure.

The algebraic stability theorem for $\mathbb{R}$-persistence modules is a fundamental result in topological data analysis. We present a stability theorem for $n$-dimensional rectangle decomposable persistence modules up to a constant…