Related papers: Normal contractive projections preserve type

The idea of a finite collection of closed sets having "strongly regular intersection" at a given point is crucial in variational analysis. We show that this central theoretical tool also has striking algorithmic consequences. Specifically,…

We work over an arbitrary ring R. Given two truncated projective resolutions of equal length for the same module we consider their underlying chain complexes. We show they may be stabilized by projective modules to obtain a pair of…

We prove that, with probability 1, all orthogonal projections of the natural measure on a percolation fractal are absolutely continuous and (except for the horizontal and vertical projection) have H\"older continuous density.

In this paper we partially address two issues: - The first is a rigidity property for pairs (S,C) consisting of a general projective K3 surface S, and a curve C obtained as the normalization of a nodal, hyperplane section of S. We prove…

We classify PBW-deformations of quadratic-constant type of certain quantizations of exterior algebras. These correspond to the fundamental modules of quantum $\mathfrak{sl}_N$, their duals, and their direct sums. We show that the first two…

We study surjective maps between the sets of all self-adjoint elements of unital $C^*$-algebras which satisfy the multiplicatively spectrum-preserving property. We show that such maps are characterized by Jordan isomorphisms and central…

We show that several important normal subgroups $\Gamma$ of the mapping class group of a surface satisfy the following property: any free, ergodic, probability measure preserving action $\Gamma \curvearrowright X$ is stably OE-superrigid.…

We introduce the notion of $*$-regular dilation for q-commuting tuples of contractions and generalize the results due to Gaspar-Suciu and Timotin on commuting contractions.

A few years ago, Richard Kadison thoroughly analysed the diagonals of projection operators on Hilbert spaces and asked the following question: Let $\mathcal{A}$ be a masa in a type $II_1$ factor $\mathcal{M}$ and let $A \in \mathcal{A}$ be…

The authors give a complete classification of projective threefolds admitting a holomorphic normal projective connection. Moreover, they prove a general structure theorem on complex projective manifolds admitting a holomorphic normal…

We prove a numerical characterization of $\mathbb{P}^n$ for varieties with at worst isolated local complete intersection quotient singularities. In dimension three, we prove such a numerical characterization of $\mathbb{P}^3$ for normal…

Currents of the SL(N) WZWN model are constrained so that the remaining symmetry is a symmetry of constrained currents as well. Such consistency enables us to study the Poisson structure of constrained SL(N) WZWN models properly. We…

An invariant kernel for the pluricanonical system of a projective manifold of general type is introduced. Using this kernel we prove that the Yau volume form on a smooth projective variety has seminegative Ricci curvature. As a biproduct we…

Let X be a smooth arithmetically Cohen-Macaulay subvariety of Pn. We prove that the restriction to X of the Veronese 3-uple embedding of Pn embeds X as a variety of wild representation type.

We find normal and seminormal forms for a sl(3)-valued zero curvature representation (ZCR). We prove a theorem about reducibility of ZCR's, which says that if one of the matrix in a ZCR (A,B) falls to a proper subalgebra of sl(3), then the…

We conjecture that a natural twisted derived category of any hyper-K\"ahler variety of $K3^{[n]}$-type is controlled by its Markman-Mukai lattice. We prove the conjecture under numerical constraints, and our proof relies heavily on…

We know that semi-regular sub-varieties satisfy the variational Hodge conjecture i.e., given a family of smooth projective varieties $\pi:\mathcal{X} \to B$, a special fiber $\mathcal{X}_o$ and a semi-regular subvariety $Z \subset…

We investigate finite non-Abelian simple groups $G$ for which the projective cover of the trivial module coincides with the permutation module on a subgroup and classify all cases unless $G$ is of Lie type in defining characteristic.

Given a singular projective variety in some projective space, we characterize the smooth curves contracted by the Gauss map in terms of normal bundles. As a consequence, we show that if the variety is normal, then a contracted line always…

Suppose F=W(k)[1/p] where W(k) is the ring of Witt vectors with coefficients in algebraically closed field k of characteristic p>2. We construct integral theory of p-adic semi-stable representations of the absolute Galois group of F with…