Related papers: On the stability of locally conformal Kaehler stru…
An introduction is provided to some current research trends in stability in geometric invariant theory and the problem of Kaehler metrics of constant scalar curvature. Besides classical notions such as Chow-Mumford stability, the emphasis…
An LCK manifold with potential is a compact quotient M of a Kahler manifold X equipped with a positive plurisubharmonic function f, such that the monodromy group acts on $X$ by holomorphic homotheties and maps f to a function proportional…
In this paper, we fix the complex structure and explore the moduli space of the heterotic system by considering two different yet "dual" deformation paths starting from a K\"ahler solution. They correspond to deformation along the…
We prove that every endomorphism which satisfies Axiom A and the strong transversality conditions is $C^1$-inverse limit structurally stable. These conditions were conjectured to be necessary and sufficient. This result is applied to the…
Motivated by the work of Cappell, Deturck, Gluch and Miller, we extend the notion of cohomology of harmonic forms (of a compact manifold with boundary) to the abstract setting of Hilbert complexes. Then, we present some geometric…
We prove that a stability condition on a K3 surface is determined by the masses of spherical objects up to a natural $\mathbb{C}$-action. This is motivated by the result of Huybrechts and the recent proposal of Bapat-Deopurkar-Licata on the…
We investigate the deformation of symmetry on cotangent bundles from the Euclidean plane to two-dimensional constant-curvature surfaces and the continuation of local dynamics aspects in Hamiltonian systems. For a fixed curvature sign…
We study homeomorphisms of tiling spaces with finite local complexity (FLC), of which suspensions of $d$-dimensional subshifts are an example, and orbit equivalence of tiling spaces with (possibly) infinite local complexity (ILC). In the…
While intersection cohomology is stable under small resolutions, both ordinary and intersection cohomology are unstable under smooth deformation of singularities. For complex projective algebraic hypersurfaces with an isolated singularity,…
The classical Cahn-Hilliard (CH) equation corresponds to a gradient dynamics model that describes phase decomposition in a binary mixture. In the spinodal region, an initially homogeneous state spontaneously decomposes via a large-scale…
We revisit the classic stability problem of the buckling of an inextensible, axially compressed beam on a nonlinear elastic foundation with a semi-analytical approach to understand how spatially localized deformation solutions emerge in…
We introduce the notion of a hamiltonian 2-form on a Kaehler manifold and obtain a complete local classification. This notion appears to play a pivotal role in several aspects of Kaehler geometry. In particular, on any Kaehler manifold with…
By proving that several new complexes of embedded disks are highly connected, we obtain several new homological stability results. Our main result is homological stability for topological chiral homology on an open manifold with…
In this paper, we provide a systematic and constructive description of Vaisman structures on certain principal elliptic bundles over complex flag manifolds. From this description we explicitly classify homogeneous l.c.K. structures on…
Roughly speaking, a conic bundle is a surface, fibered over a curve, such that the fibers are conics (not necessarily smooth). We define stability for conic bundles and construct a moduli space. We prove that (after fixing some invariants)…
We study the Bridgeland stability of line bundles on surfaces using Bridgeland stability conditions determined by divisors. We show that given a smooth projective surface $S$, a line bundle $L$ is always Bridgeland stable for those…
We study the conditions under which a K\"ahlerian structure $(G,J)$ of general natural lift type on the cotangent bundle $T^*M$ of a Riemannian manifold $(M,g)$ has constant holomorphic sectional curvature. We obtain that a certain…
This paper investigates the wall structure of the space of stability conditions on Hirzebruch surfaces. Using the gluing construction of \cite{CP} and \cite{Uch} with respect to a fixed semiorthogonal decomposition, we focus on two main…
Our aim here is to investigate the holomorphic geometric structures on compact complex manifolds which may not be K\"ahler. We prove that holomorphic geometric structures of affine type on compact Calabi-Yau manifolds with polystable…
A projective variety has a large fundamental group if its universal covering has no compact subvarieties. In this paper we investigate whether the property of a variety having a large fundamental groups is stable under K\"{a}hler…