Related papers: On some $\cal D$-modules in dimension 2

In this paper we study various convolution-type algebras associated with a locally compact quantum group from cohomological and geometrical points of view. The quantum group duality endows the space of trace class operators over a locally…

We present a geometric proof for the duality theorem of linear programming. Besides being self-contained and simple, the present approach also provides a transparent way for understanding this fundamental result.

In the present paper 2-local derivations on various algebras of infinite dimensional matrix-valued functions on a compact are considered. It is proved that every 2-local derivation on such algebra is a derivation. Also we explain that the…

We study the value distribution of holomorphic curves from a general open Riemann surface into a smooth logarithmic pair $(X, D).$ By stochastic calculus, we first obtain a version of tautological inequality (proposed by McQuillan) and a…

This manuscript represents an advance in the enumerative geometry of opers that takes the subject beyond our previous work. Motivated by a counting problem of linear differential equations in positive characteristic, we investigate the…

We produce a new proof of Tao's result on the slightly supercritical Navier Stokes equations. Our proof has the advantage that it works in the plane while Tao's proof works only in dimensions three and higher. We accomplish this by studying…

Let $ \mathcal{D} = \{D_{1}, \ldots, D_{\ell}\} $ be an arrangement of smooth hypersurfaces with normal crossings on the complex projective space $ \mathbb{P}^{n} $ and let $ \Omega^{1}_{\mathbb{P}^{n}}(log \mathcal{D}) $ be the logarithmic…

We show that if $\Lambda$ is a $n$-Koszul algebra and $E=E(\Lambda)$ is its Yoneda algebra, then there is a full subcategory $\mathcal{L}_E$ of the category $Gr_E$ of graded $E$-modules, which contains all the graded $E$-modules presented…

We show that the moduli space M(r,c) of semistable sheaves on n-dimensional projective space with support of dimension one, with multiplicity r and with Euler characteristic c is isomorphic to M(r,-c).

Given a two-variable function $f$ without critical points and a compact region $R$ bounded by two level curves of $f$, this note proves that the integral over $R$ of the second-order directional derivative of $f$ in the tangential…

We introduce a version of Koszul duality for categories, which extends the Koszul duality of operads and right modules. We demonstrate that the derivatives which appear in Weiss calculus (with values in spectra) form a right module over the…

Let p be a prime number. We compute the Yoneda extension algebra of $GL_2$ over an algebraically closed field of characteristic p by developing a theory of Koszul duality for a certain class of 2-functors, one of which controls the category…

We consider the Lie-algebra of the group of diffeomorphisms of d-dimensional torus which is also known to be the algebra of derivations on a Laurent polynomial ring A in d commuting variables denoted by DerA. Larsson has constructed a large…

We prove that two cusps of the same dimension in the Baily-Borel compactification of some classical series of modular varieties are linearly dependent in the rational Chow group of the compactification. This gives a higher dimensional…

We introduce the notion of being cohomologically complete for objects of the derived category of sheaves of $Z[\hbar]$-modules on a topological space. Then we consider a $Z[\hbar]$-algebra satisfying some suitable conditions and prove…

We study the behaviour of ordinary parts of the homology modules of modular curves, associated to a decreasing sequence of congruence subgroups ${\Gamma}_1(N2^r)$ for $r \geq 2$, and prove a control theorem for these homology modules.

Let $X$ be a compact Riemann surface of genus $g \geq 3$. We consider the moduli space of holomorphic connections over $X$ and the moduli space of logarithmic connections singular over a finite subset of $X$ with fixed residues. We…

In a previous paper we showed that for every polarization on an abelian variety there is a dual polarization on the dual abelian variety. In this note we extend this notion of duality to families of polarized abelian varieties. As a main…

We prove a boundedness criterion for a class of dyadic multilinear forms acting on two-dimensional functions. Their structure is more general than the one of classical multilinear Calder\'{o}n-Zygmund operators as several functions can now…

We prove a duality theorem for certain graded algebras and show by various examples different kinds of failure of tameness of local cohomology.