相关论文: Some applications of microlocalization for local c…

We provide a structure theorem for all almost complete intersection ideals of depth three in any Noetherian local ring. In particular, we find that the minimal generators are the pfaffians of suitable submatrices of an alternating matrix.…

In this note, we derive a uniqueness theorem for minimal graphs of general codimension under certain restrictions closed related to the convexity (not strict convexity) of the area functional with respect to singular values, improving the…

Let M be a connection on a complex affine space with poles along a hyperplane. In this paper, we prove that the nearby cycles of Abbes and Saito's construction applied to M satisfy a linearity condition analogous to that obtained by Abbes…

We construct non-flat minimal capillary cones with bi-orthogonal symmetry groups for any dimension and contact angle. These cones interpolate between rescalings of a singular solution to the one-phase problem and the free-boundary cone…

Fano varieties are subvarieties of the Grassmannian whose points parametrize linear subspaces contained in a given projective variety. These expository notes give an account of results on Fano varieties of complete intersections, with a…

The main aim of the paper is to provide analogues of Simpson's correspondence on singular projective varieties defined over an algebraically closed field of characteristic $p>0$. There are two main cases. In the first case, we consider…

Let $(Q, \mathfrak{n})$ be a regular local ring and let $f_1, \ldots, f_c \in \mathfrak{n}^2$ be a $Q$-regular sequence. Set $(A, \mathfrak{m}) = (Q/(\mathbf{f}), \mathfrak{n}/(\mathbf{f}))$. Further assume that the initial forms $f_1^*,…

This paper establishes a general topological condition under which the semilocal stability of a set-valued mapping can be exactly determined by its local stability properties. Specifically, we investigate the relationship between the…

We propose a three-dimensional field theory construction that realizes the vertex algebras associated with the intermediate Lie algebras and the related $C_2$-cofinite minimal $W$-algebras of the Deligne-Cvitanovi\'c (DC) series as boundary…

The paper introduces and characterizes new notions of Lipschitzian and H\"olderian full stability of solutions to general parametric variational systems described via partial subdifferential and normal cone mappings acting in Hilbert…

The purpose of this paper is to study microlocal conditions for inclusion relations between the ranges of square systems of pseudodifferential operators which fail to be locally solvable. The work is an extension of earlier results for the…

In a recent article, we described how the microscopic structure of density-density correlations in the fluid interfacial region, for systems with short-ranged forces, can be understood by considering the resonances of the local structure…

The geometric Satake equivalence and the Springer correspondence are closely related when restricting to small representations of the Langlands dual group. We prove this result for \'etale sheaves, including the case of the mixed…

Intersection homology is obtained from ordinary homology by imposing conditions on how the embedded simplices meet the strata of a space $X$. In this way, for the middle perversity, properties such as strong Lefschetz are preserved. This…

We present a construction of regular Stein neighborhoods of a union of maximally totally real subspaces $M=(A+iI)\mathbb{R}^n$ and $N=\mathbb{R}^n$ in $\mathbb{C}^n$, provided that the entries of a real $n \times n$ matrix $A$ are…

Our goal is to analyse singularities of integral models of Shimura varieties. One approach is to construct local models, which model the singularities of the corresponding integral model using linear algebra dada and find resolutions with…

A left invariant metric on a nilpotent Lie group is called minimal, if it minimizes the norm of the Ricci tensor among all left invariant metrics with the same scalar curvature. Such metrics are unique up to isometry and scaling and the…

We are interested in the intersection cohomology of the minimal compactification of Siegel modular varieties at some places of bad reduction. We compute the semi-simple trace of the Frobenius morphism on the fibers of the nearby cycles of…

In this work we perform a general study of properties of a class of locally symmetric embedded hypersurfaces in spacetimes admitting a $1+1+2$ spacetime decomposition. The hypersurfaces are given by specifying the form of the Ricci tensor…

This survey is about old and new results about the modular representation theory of finite reductive groups with a strong emphasis on local methods. This includes subpairs, Brauer's Main Theorems, fusion, Rickard equivalences. In the…