Related papers: Linear spaces of rational integrable 1-forms

In this short note we present several infinite dimensional theorems which generalize corresponding facts from the finite dimensional differential inclusions theory.

We study the cohomology of the space of immersed genus g surfaces in a simply-connected manifold. We compute the rational cohomology of this space in a stable range which goes to infinity with g. In fact, in this stable range we are also…

Motivated by recent results on radial projections and applications to the celebrated Falconer distance problem, we study radial projections in the setting of finite fields. More precisely, we extend results due to Mattila and Orponen…

We describe the irreducible components of the moduli spaces of rational curves on Artin-Mumford double solids. This provides the first example of Fano varieties that satisfy Geometric Manin's Conjecture with multiple Manin components in…

Let $M_1$ and $M_2$ be closed connected orientable $3$-manifolds. We classify the sets of smooth and piecewise linear isotopy classes of embeddings $M_1\sqcup M_2\rightarrow S^6$.

In this paper we classify irreducible integrable representations of loop toroidal Lie algebras with finite dimensional weight spaces. In both the cases we classify modules, when a part of center acts non-trivially and trivially on modules.

We investigate when the tangent bundle of a projective manifold has a non-trivial first order (or positive-dimensional) deformation. This leads to a new conjectural characterization of the complex projective space.

We study the space of deformations of a smooth foliation of the 5-sphere by complex manifolds

We calculate a projective space of essential measured laminations in a surface pair, which will be used in another paper to help describe spaces of "finite height laminations."

We prove that every irreducible component of semi-regular loci of effective line bundles in the Picard scheme of a smooth projective variety has at worst rational singularities. This generalizes Kempf's result on rational singularities of…

The goal of this work is to extend Dirac-type tensor equations to a curved space. We take four 1-forms (a tetrad) as a unique structure, which determines a geometry of space-time.

Let $\Lambda$ be a basic finite dimensional algebra over an algebraically closed field, presented as a path algebra modulo relations; further, assume that $\Lambda$ is graded by lengths of paths. The paper addresses the classifiability, via…

The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…

A solution to the problem of topological classification of real cubic fourfolds is presented. It is shown that the real locus of a real non-singular cubic fourfold is obtained from a projective 4-space either by adding several trivial one-…

We prove that if a linear equation, whose coefficients are continuous rational functions on a nonsingular real algebraic surface, has a continuous solution, then it also has a continuous rational solution. This is known to fail in higher…

The moduli spaces of compact and connected Riemann surfaces has been a central topic in modern mathematics in recent years. Thus their homological dimensions become important invariants. Motivated by the emergence mathematical counterparts…

This is the first in a pair of papers developing a framework for the application of logarithmic structures in the study of singular curves of genus $1$. We construct a smooth and proper moduli space dominating the main component of…

In this paper, we systematically investigate the geometry and topology of manifolds with integral radial curvature bounds, and obtain many interesting and important conclusions.

A complete classification and character formulas for finite-dimensional irreducible representations of the rational Cherednik algebra of type A is given. Less complete results for other types are obtained. Links to the geometry of affine…

We study the weighted Fock spaces in one and several complex variables. We evaluate the dimension of these spaces in terms of the weight function extending and completing earlier results by Rozenblum-Shirokov and Shigekawa.