Related papers: Ueda's lemma via uniform H\"ormander estimates for…

We prove continuity results for new stability thresholds related to uniform K-stability and deduce that uniform K-stability is an open condition in the K\"ahler cone of any compact K\"ahler manifold, thus establishing an algebro-geometric…

The purpose of this paper is to investigate canonical metrics on a semi-stable vector bundle E over a compact Kahler manifold X. It is shown that, if E is semi-stable, then Donaldson's functional is bounded from below. This implies that E…

We prove the generalized Obata theorem on foliations. Let M be a complete Riemannian manifold with a foliation F of codimension $q>1$ and a bundle-like metric. Then $(M, F)$ is transversally isometric to the q-sphere of radius 1/c in…

We study the behavior of cohomological support loci of the canonical bundle under derived equivalence of smooth projective varieties. This is achieved by investigating the derived invariance of a generalized version of Hochschild homology.…

We present closed form expressions for the ranks of all cohomology groups of holomorphic line bundles on several Calabi-Yau threefolds realised as complete intersections in products of projective spaces. The formulae have been obtained by…

We prove a global uniform Artin-Rees lemma type theorem for sections of ample line bundles over smooth projective varieties. This result is used to prove an Artin-Rees lemma for the polynomial ring with uniform degree bounds. The proof is…

We give several generalizations of the Kodaira vanishing and embedding theorems for K\"ahler manifolds to the case where the relevent line bundle has a small region of negative curvature. To prove the vanishing theorems we adapt techniques…

We prove general type results for orthogonal modular varieties associated with the moduli of compact hyperk\"ahler manifolds of deformation generalised Kummer type ('deformation generalised Kummer varieties'). In particular, we consider…

In 1980 Michelsohn defined a differential operator on sections of the complex Clifford bundle over a compact K\"ahler manifold M . This operator is a differential and its Laplacian agrees with the Laplacian of the Dolbeault operator on…

We give local criteria for smooth non-embeddablity of Levi-flat manifolds. For this purpose, we pose an analogue of Ueda theory on the neighborhood structure of hypersurfaces in complex manifolds with topologically trivial normal bundles.

In arXiv:1710.01672, we obtained general type results for orthogonal modular varieties associated with moduli spaces of compact hyperk\"ahler manifolds of deformation generalised Kummer type (also known as 'deformation generalised Kummer…

These are lecture notes for a course to be held. They provide a full discussion of certain analytic aspects of the uniformisation theory of (singular) holomorphic foliations by curves on compact Kaehler manifolds, with emphasis on their…

Let $X$ be a compact Riemann surface of genus $g\geq 2$ equipped with flat conical metric $|\Omega|$, where $\Omega$ be a holomorphic quadratic differential on $X$ with $4g-4$ simple zeroes. Let $K$ be the canonical line bundle on $X$.…

In this paper, we investigate the H\"ormander type theorems for the multi-linear and multi-parameter Fourier multipliers. When the multipliers are characterized by $L^u$-based Sobolev norms for $1<u\le 2$ , our results on the smoothness…

Let $M$ be a compact manifold. and $D$ a Dirac type differential operator on $M$. Let $A$ be a $C^*$-algebra. Given a bundle $W$ of $A$-modules over $M$ (with connection), the operator $D$ can be twisted with this bundle. One can then use a…

In this note, we propose an approach to the study of the analogue for unipotent harmonic bundles of Schmid's Nilpotent Orbit Theorem. Using this approach, we construct harmonic metrics on unipotent bundles over quasi-compact K\"ahler…

Concerned with elliptic operators with stationary random coefficients governed by linear or nonlinear mixing conditions and bounded (or unbounded) $C^1$ domains, this paper mainly studies (weighted) annealed Calder\'on-Zygmund estimates,…

In this article we consider linear operators satisfying a generalized commutation relation of a type of the Heisenberg-Lie algebra. It is proven that a generalized inequality of the Hardy's uncertainty principle lemma follows. Its…

Let $X$ be a complex manifold and $L$ be a holomorphic line bundle on $X$. Assume that $L$ is semi-positive, namely $L$ admits a smooth Hermitian metric with semi-positive Chern curvature. Let $Y$ be a compact K\"ahler submanifold of $X$…

We formalize the ``metric bundle'' viewpoint by defining, for any smooth $n$--manifold $M$, the open fiberwise cones $\mathcal{G}^{p,q}\subset S^2\Tstar M$ of nondegenerate symmetric bilinear forms with fixed signature $(p,q)$, and we…