相关论文: On a question of Koll\'{a}r
In the first part of this paper, we study the properties of some particular plurisubharmonic functions, namely the toric ones. The main result of this part is a precise description of their multiplier ideal sheaves, which generalizes the…
The goal of this note is to present some recent results of our research concerning multiplier ideal sheaves on complex spaces and singularities of plurisubharmonic functions. We firstly introduce multiplier ideal sheaves on complex spaces…
As an application of the residue functions corresponding to the lc-measures developed by the authors, the proof of the injectivity theorem on compact K\"ahler manifolds for plt pairs by Matsumura is improved in this article to allow…
We study analytic function interpolating the multiple generalized Euler numbers attached to $\chi$ at negative integers.
A new definition of analytic adjoint ideal sheaves for quasi-plurisubharmonic (quasi-psh) functions with only neat analytic singularities is studied and shown to admit some residue short exact sequences which are obtained by restricting…
The present work deals with the mathematical investigation of some generalizations of the Sz\'{a}sz operators. In this work, the multiple Sheffer polynomials are introduced. The generalization of Sz\'{a}sz operators involving multiple…
We prove a result on the inversion of adjunction for log canonical pairs that generalizes Kawakita's result to log canonical centers of arbitrary codimension.
In this note, we show how to apply the original $L^2$-extension theorem of Ohsawa and Takegoshi to the standard basis of a multiplier ideal sheaf associated with a plurisubharmonic function. In this way, we are able to reprove the strong…
In the present article, we obtain an optimal support function of weighted $L^2$ integrations on superlevel sets of psh weights, which implies the strong openness property of multiplier ideal sheaves.
In this article, we will present that the analytic adjoint ideal sheaves associated to plurisubharmonic functions are not coherent.
We generalize Koll\'ar's conjecture (including torsion freeness, injectivity theorem, vanishing theorem and decomposition theorem) to Saito's $S$-sheaves twisted by a $\mathbb{Q}$-divisor. This gives a uniform treatment for various kinds of…
We analyze adjunction and inversion of adjunction for the $F$-purity of divisor pairs in characteristic $p > 0$. In this vein, we give a complete answer for principal divisors under $\mathbb{Q}$-Gorenstein assumptions but without…
Schur functions satisfy the relative Pl\"ucker relations which describe the projective embedding of the flag varieties and the Hirota bilinear equations for the modified KP hierarchies. These relative Pl\"ucker relations are generalized to…
We prove a Thullen type extension theorem of plurisubharmonic functions across a closed complete pluripolar set, which generalizes a theorem of Siu. Our approach depends on an Ohsawa-Takegoshi type extension theorem for a single point in a…
We begin a systematic investigation of universal norms for $p$-adic representations in higher rank Iwasawa theory. After establishing the basic properties of the module of higher rank universal norms we construct an Iwasawa-theoretic…
In this article we prove analogs of Kawamata's canonical bundle formula, Kawamata subadjunction and plt/lc inversion of adjunction for generalized pairs on Kaehler varieties. We also show that a conjecture of BDPPin dimension n-1 implies…
In this paper, I prove a very general extension theorem for log pluricanonical systems. The main application of this extension theorem is (together with Kawamata's subadjunction theorem) to give an optimal subadjunction theorem which…
The main goal of this paper is to construct an algebraic analogue of quasi-plurisubharmonic function (qpsh for short) from complex analysis and geometry. We define a notion of qpsh function on a valuation space associated to a quite general…
The purpose of this article is to give a Chlodowsky type generalization of Szasz operators defined by means of the Sheffer type polynomials. We obtain convergence properties of our operators with the help of Korovkin's theorem and the order…
A result of Bleher, Chinburg, Greenberg, Kakde, Pappas, Sharifi and Taylor has initiated the topic of higher codimension Iwasawa theory. As a generalization of the classical Iwasawa main conjecture, they prove a relationship between…