Related papers: Multiplier ideal sheaves, complex singularity expo…
We consider the restriction and induction of representations between a covering group and its derived subgroup, both on the representation-theoretic side and the L-parameter side. In particular, restriction of a genuine principal series is…
We obtain a sufficient condition for boundary regularity of quasiminimizers of the p-energy integral in terms of a Wiener type sum of power type. The exponent in the sum is independent of the dimension and is explicitly expressed in terms…
Fix nonzero ideal sheaves a_1,...,a_r on a normal Q-Gorenstein complex variety X. Fix any positive real number c, and consider the multiplier ideal J of the sum a_1+...+a_r with weighting coefficient c. We construct an exact sequence…
In this paper, we prove a version of weighted inequalities of exponential type for fractional integrals with sharp constants in any domain of finite measure in $\mathbb{R}^{n}$. Using this we prove a sharp singular Adams inequality in high…
The purpose of this note is to discuss several results that have been obtained in the last decade in the context of sharp adjoint Fourier restriction/Strichartz inequalities. Rather than aiming at full generality, we focus on several…
In this article, we present that for any complex manifold whose dimension is bigger than one, there exists a multiplier ideal sheaf such that there don't exist equisingular weights with logarithmic poles, which are not smaller than the…
An old conjecture of Durfee 1978 bounds the ratio of two basic invariants of complex isolated complete intersection surface singularities: the Milnor number and the singularity (or geometric) genus. We give a counterexample for the case of…
In this paper, we study the coherence of a higher rank analogue of a multiplier ideal sheaf. Key tools of the study are H\"ormander's $L^2$-estimate and a singular version of a Demailly--Skoda type result.
We show that the relation between multiplier ideals and $V$-filtration on the structure sheaf due to Budur-Musta\c{t}\u{a}-Saito generalizes to singular irreducible varieties, by replacing multiplier ideals with multiplier modules and the…
In this article, we show that if $X$ is an excellent surface with rational singularities, the constant sheaf $\mathbb{Q}_{\ell}$ is a dualizing complex. In coefficient $\mathbb{Z}_{\ell}$, we also prove that the obstruction for…
Let $A$ be an excellent two-dimensional normal local ring containing an algebraically closed field and let $X\to \mathrm{Spec} (A)$ be a resolution of singularity. We prove a theorem giving a condition under which the dimension of the…
We describe a relation between two invariants that measure the complexity of a hypersurface singularity. One is the Hodge spectrum which is related to the monodromy and the Hodge filtration on the cohomology of the Milnor fiber. The other…
Recently, H. Dao and R. Nair gave a combinatorial description of simplicial complexes $\Delta$ such that the squarefree reduction of the Stanley-Reisner ideal of $\Delta$ has the WLP in degree $1$ and characteristic zero. In this paper, we…
In this paper, we explore the geometry of potential triples $(X,\Delta,D)$, which by definition consists of a pair $(X,\Delta)$ and an $\mathbb{R}$-Cartier pseudoeffective divisor $D$ on $X$. We define and study the asymptotic multiplier…
Shearer's inequality bounds the sum of joint entropies of random variables in terms of the total joint entropy. We give another lower bound for the same sum in terms of the individual entropies when the variables are functions of…
We consider abstract non-negative self-adjoint operators on $L^2(X)$ which satisfy the finite speed propagation property for the corresponding wave equation. For such operators we introduce a restriction type condition which in the case of…
This paper deals with properties of the algebraic variety defined as the set of zeros of a "typical" sequence of polynomials. We consider various types of "nice" varieties: set-theoretic and ideal-theoretic complete intersections,…
It was recently established by the first two authors that multiplier ideals on a smooth variety satisfy some special syzygetic properties. The purpose of this note is to show how some of these can be extended to the singular setting.
This paper deals with the subject of infinitesimal variations of Euclidean submanifolds with arbitrary dimension and codimension. The main goal is to establish a Fundamental theorem for these geometric objects. Similar to the theory of…
We present a conjecture on multiplicity of irreducible representations of a subgroup $H$ contained in the irreducible representations of a group $G$, with $G$ and $H$ having the same derived groups. We point out some consequences of the…