Published in Bollettino dell'Unione Matematica Italiana
We prove the equisingular rigidity of the singular Hirzebruch–Kummer coverings X(n, L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {L}$$\end{document}) of th...
Published in Georgian Mathematical Journal
Using homological perturbation theory, we develop a formal version of the miniversal deformation associated with a deformation problem controlled by a differential graded Lie algebra over a field of characteristic zero. Our approach includes a formal version of the Kuranishi method in the theory of deformations of complex manifolds.
Published in Mathematische Zeitschrift
If X is a rational surface without nonzero holomorphic vector field and f is an automorphism of X, we study in several examples the Zariski tangent space of the local deformation space of the pair (X, f).
Published in Advances in Pure and Applied Mathematics
Let G be a type 1 connected and simply connected solvable Lie group. The generalized moment map for π in G^{\widehat{G}}, the unitary dual of G, sends smooth vectors of the representation space of π to 𝒰(𝔤)*{{\mathcal{U}(\mathfrak{g})}^{*}}, the dual vector space of 𝒰(𝔤){\mathcal{U}(\mathfrak{g})}. The convex hull of the image of the generalized ...
Published in Mathematische Annalen
We prove that for a compact Kähler threefold with canonical singularities and vanishing first Chern class, the projective fibres are dense in the semiuniversal deformation space. This implies that every Kähler threefold of Kodaira dimension zero admits small projective deformations after a suitable bimeromorphic modification. As a corollary, we see...
Published in Annals of Global Analysis and Geometry
We describe the generalized Kuranishi spaces of solvmanifolds with left-invariant complex structures. By using such description, we study the stability of left-invariantness of deformed generalized complex structures and smoothness of generalized Kuranishi spaces on certain classes of solvmanifolds. We also give explicit finite-dimensional cochain ...
Published in Acta Mathematica Sinica, English Series
We present a construction of globally convergent power series of integrable Beltrami differentials on the Ricci-flat \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pa...
Published in Advances in Pure and Applied Mathematics
So far, the uncertainty principles for solvable non-exponential Lie groups have been treated only in few cases. The first author and Kaniuth produced an analogue of Hardy's theorem for a diamond Lie group, which is a semi-direct product of ℝd with the Heisenberg group ℍ 2d+1 ${\mathbb {H}_{2d+1}}$ In this setting, we formulate and prove in this pap...
Published in Advances in Pure and Applied Mathematics
Let ℍ2n+1r be the reduced Heisenberg Lie group, G = ℍ2n+1r × ℍ2n+1r be the (4n + 2)-dimensional Lie group and ΔG = {(x,x) ∈ G : x ∈ ℍ2n+1r} be the diagonal subgroup of G. Given any discontinuous subgroup Γ ⊂ G for G/ΔG, we provide a layering of the parameter space ℛ(Γ, G, ΔG), which is shown to be endowed with a smooth manifold structure, we also s...
Published in The Journal of Geometric Analysis
We classify invariant complex structures on 6-dimensional nilmanifolds up to equivalence. As an application, the behavior of the associated Frölicher sequence is studied as well as its relation to the existence of strongly Gauduchon metrics. We also show that the strongly Gauduchon property and the balanced property are not closed under holomorphic...
