Related papers: A Bergman kernel proof of the Kawamata subadjuncti…

In this article, we obtain an Ohsawa-Takegoshi-type $L^2$-extension for upper semi-continuous $L^2$-optimal functions via a Lebesgue-type differentiation theorem. As applications, we give a characterization of plurisubharmonic functions via…

The goal of this survey is to describe some recent results concerning the L 2 extension of holomorphic sections or cohomology classes with values in vector bundles satisfying weak semi-positivity properties. The results presented here are…

We treat a relative version of the main theorem in my previous paper: A transcendental approach to Koll\'ar's injectivity theorem. More explicitly, we give a curvature condition that implies Koll\'ar type cohomology injectivity theorems in…

For a continuous function, we prove that the function is pluriharmonic if and only if the equality part of the optimal Ohsawa--Takegoshi $L^2$-extension theorem is satisfied with respect to the metric having the function as a weight. This…

We first prove a Cauchy's integral theorem and Cauchy type formula for certain inhomogeneous Cimmino system from quaternionic analysis perspective. The second part of the paper directs the attention towards some applications of the…

Here we discuss a new simplified proof of the essential self-adjointness for formally self-adjoint differential operators of real principal type, previously proved by Vasy (2020) and Nakamura-Taira (2021). For simplicity, here we discuss…

We show that under suitable hypothesis (which are sharp in certain sense) that the core of an m-primary ideal in a regular local ring of dimension d is equal to the adjoint (or multiplier) ideal of its d-th power, generalizing a result of…

We give a complete proof of results announced by Hirasawa and Sakuma describing explicitly the Kakimizu complex of a non-split, prime, special, alternating link.

We show how ideas from \cite{2Blocki} and \cite{3Blocki} to prove the Suita conjecture can be adapted to give a proof of the Ohsawa-Takegoshi extension theorem with sharp estimates.

Generalizing and strengthening a recent result of Koziarz, we prove a version of the Ohsawa-Takegoshi-Manivel theorem for $\dbar$-closed forms.

We prove the Strengthened Hanna Neumann Conjecture. We give a more direct cohomological interpretation of the conjecture in terms of "typical" covering maps, and use graph Galois theory to "symmetrize" the conjecture. The conjecture is then…

We give a direct proof of the Ohsawa-Takegoshi by solving directly the d-bar equation.

Let $(\mathcal{B},\mathcal{A}, i, e, l)$ be a cleft extension of abelian categories. We prove that the functor $l$ preserves and reflects (Wakamatsu) tilting pairs of subcategories under certain conditions, unifying an abundance of known…

The purpose of this paper is to report on the unpublished manuscript [O] by T. Okuyama where are proved some conjectures generalizing to homotopy categories the theorems of [CaRi] and [LS] holding in derived categories. We refer to the…

Our main theorem is an extension of the well-known Mizoguchi-Takahaashi's fixed point theorem [N. Mizogochi and W. Takahashi, Fixed point theorems for multi-valued mappings on complete metric space, {\it J. Math. Anal. Appl.} 141 (1989)…

We prove the Mumford-Tate conjecture for those abelian varieties over number fields, whose simple factors of their adjoint Mumford-Tate groups have over $\dbR$ certain (products of) non-compact factors. In particular, we prove this…

We give a formal account of B\'enabou's theorem for peudoadjunctions in the context of Gray-categories. We prove that to give a pseudoadjunction $F \dashv U: A \to X$ with unit $\eta$ in a Gray-category K is precisely to give an absolute…

We prove new pointwise bounds for weighted Bergman kernels in $\mathbb{C}^n$, whenever a coercivity condition is satisfied by the associated weighted Kohn Laplacian on $(0,1)$-forms. Our results extend the ones obtained in $\mathbb{C}$ by…

We establish a new Iwasawa theory for the kernel of Frobenius on Jacobians of curves in geometric $\mathbf{Z}_p$-towers over the projective line in characteristic $p$, thereby proving several of the main conjectures of [arXiv:2107.12555].

Let $(X, \omega)$ be a weakly pseudoconvex K\"ahler manifold, $Y \subset X$ a closed submanifold defined by some holomorphic section of a vector bundle over $X,$ and $L$ a Hermitian line bundle satisfying certain positivity conditions. We…