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A generalization of von Staudt's theorem that every permutation of the projective line that preserves harmonic quadruples is a projective semilinear map is given. It is then concluded that any proper supergroup of permutations of the…

Simple derivation of the classical generalized Moller-Wu-Lee transformations from general master equation is presented.We will argue that in fact we can implement Born's notion of rigid motion in both flat spacetime and arbitrary curved…

Let Q be an affine quiver of type A. Let C be the associated generalized Cartan matrix. Let U^- be the negative part of the quantized enveloping algebra attached to C. In terms of perverse sheaves on the moduli space of representations of a…

We construct projective moduli spaces for torsion-free sheaves on noncommutative projective planes. These moduli spaces vary smoothly in the parameters describing the noncommutative plane and have good properties analogous to those of…

We show that, among all smooth one-dimensional maps conjugated to an N-ary shift (a Bernoulli shift of N symbols), Chebyshev maps are distinguished in the sense that they have least higher-order correlations. We generalise our consideration…

Let $L$ and $L'$ be two invertible sheaves over a projective variety $X$. We suppose that $L$ and $L'$ are generated by their global section spaces $\Gamma(L)$ and $\Gamma(L')$. We prove in this article that the morphism : \[\Gamma(L)…

We study the perturbative path integral of Chern-Simons theory (the effective BV action on zero-modes) in Lorenz gauge, expanded around a (possibly non-acyclic) flat connection, as a family over the smooth irreducible stratum $\mathcal{M}'…

Let $\cal A$ be a maximal (or more generally a hereditary) order in a central simple algebra over a global field $F$ of positive characteristic. We study the reduction of the modular scheme of $\cal A$-elliptic sheaves at all places of $F$.…

We analyze irreducible perverse sheaves on abelian varieties, defined over the complex numbers or the algebraic closure of a finite field, whose Euler characteristic is zero. We give a description of such perverse sheaves under assumptions…

We introduce a Bredon motivic cohomology theory for smooth schemes defined over a field and equipped with an action by a finite group. These cohomology groups are defined for finite dimensional representations as the hypercohomology of…

Let $f$ be a morphism from a klt pair $(X, \Delta)$ to an abelian variety $A$, $m\geq1$ a rational number and $D$ a Cartier divisor on $X$ such that $D\sim_{\mathbb Q}m(K_X+\Delta)$. We prove that the sheaf $f_*\mathcal{O}_X(D)$ becomes…

For a smooth projective variety $X\subseteq \mathbb P^N$ over an algebraically closed field of char $0$, we show that the discriminant locus of a generic projection of $X$ is projectively dual to a general linear section of the dual…

We give a new and intrinsic proof of the transitivity of the braid group action on the set of full exceptional sequences of coherent sheaves on a weighted projective line. We do not use here the corresponding result of Crawley-Boevey for…

We define a generalization of the Mullineux involution on multipartitions using the theory of crystals for higher level Fock spaces. Our generalized Mullineux involution turns up in representation theory via two important derived functors…

We suggest a possibility for a categorical generalization of the concept of a perverse sheaf, in which vector spaces are replaced by triangulated categories. We call such hypothetical objects perverse Schobers and consider several examples,…

One of the major open problems in noncommutative algebraic geometry is the classification of noncommutative projective surfaces (or, slightly more generally, of noetherian connected graded domains of Gelfand-Kirillov dimension 3). In a…

For complex projective varieties, all natural transformations from constructible functions to homology (modulo torsion) are linear combinations of the MacPherson-Schwartz-Chern classes. (The authors are willing to mail hard copies of the…

This is the second of series of papers studyig moduli spaces of a certain class of coherent sheaves, which we call stable perverse coherent sheaves, on the blow-up of a projective surface at a point. The followings are main results of this…

Let $\sigma$ be arc-length measure on $S^1\subset \mathbb R^2$ and $\Theta$ denote rotation by an angle $\theta \in (0, \pi]$. Define a model bilinear generalized Radon transform, $$B_{\theta}(f,g)(x)=\int_{S^1} f(x-y)g(x-\Theta y)\,…

The goal of this paper is to generalize several basic results from the theory of $\cal{D}$-modules to the representation theory of rational Cherednik algebras. We relate characterizations of holonomic modules in terms of singular support…