Related papers: The d-bar-equation on homogeneous varieties with a…

The goal of this paper is to set up an obstruction theory in the context of algebras over an operad and in the framework of differential graded modules over a field. Precisely, the problem we consider is the following: Suppose given two…

In this paper we address the following question: is it always possible to choose a deformation quantization of a Poisson algebra A so that certain Poisson-commutative subalgebra C in it remains commutative? We define a series of…

We compute the algebra of differential invariants of unparametrized curves in the homogeneous G(2) flag varieties, namely in G(2)/P. This gives a solution to the equivalence problem for such curves. We consider the cases of integral and…

The p-cohomology of an algebraic variety in characteristic p lies naturally in the category $D_{c}^{b}(R)$ of coherent complexes of graded modules over the Raynaud ring (Ekedahl-Illusie-Raynaud). We study homological algebra in this…

We develop an obstruction theory for homotopy of homomorphisms f,g : M -> N between minimal differential graded algebras. We assume that M = Lambda V has an obstruction decomposition given by V = V_0 oplus V_1 and that f and g are homotopic…

We consider solutions of Lagrangian variational problems with linear constraints on the derivative. These solutions are given by curves $\gamma$ in a differentiable manifold $M$ that are everywhere tangent to a smooth distribution $\mathcal…

We present an argument due to Thom to formulate a priori cohomology obstructions for a projective variety to admit an embedded resolution of singularities, and generalize the argument to a field of characteristic $p > 0$. We show that these…

We find the R matrix for the inhomogeneous quantum groups whose homogeneous part is $GL_q(n)$, or its restrictions to $SL_q(n)$,$U_q(n)$ and $SU_q(n)$. The quantum Yang-Baxter equation for R holds because of the Hecke relation for the…

Let $K$ be a field of characteristic $\ne 2$ and let $X$ be the affine variety over $K$ defined by the equation $$ X:\ a_0x_0^2 + \cdots + a_nx_n^2 = 1 $$ where $n\ge 0$ and $a_i\in K$. In this paper we compute the lowest mod 2 \'{e}tale…

We study deformations of pairs (X,D), with X smooth projective variety and D a smooth or a normal crossing divisor, defined over an algebraically closed field of characteristic 0. Using the differential graded Lie algebras theory and the…

Let V_0 and V_1 be complex vector bundles over a space X. We use the theory of divisors on formal groups to give obstructions in generalised cohomology that vanish when V_0 and V_1 can be embedded in a bundle U in such a way that V_0\cap…

We give an interpretation of the Brauer group of a purely inseparable extension of exponent 1, in terms of restricted Lie-Rinehart cohomology. In particular, we define and study the category $p$-$\rm{LR}(A)$ of restricted Lie-Rinehart…

We study $d$-dimensional simplicial complexes that are PL embeddable in $\mathbb{R}^{d+1}$. It is shown that such a complex must satisfy a certain homological condition. The existence of this obstruction allows us to provide a systematic…

We consider a problem of mixed Cauchy type for certain holomorphic partial differential operators whose principal part $Q_{2p}(D)$ essentially is the (complex) Laplace operator to a power, $\Delta^p$. We pose inital data on a singular conic…

The aim of this article is to study the $L^{p}$-boundedness of pseudo-differential operators on a homogeneous tree $ \mathfrak{X} $. For $p\in (1,2)$, we establish a connection between the $L^{p}$-boundedness of the pseudo-differential…

Let $Y$ be a smooth curve embedded in a complex projective manifold $X$ of dimension $n\geq 2$ with ample normal bundle $N_{Y|X}$. For every $p\geq 0$ let $\alpha_p$ denote the natural restriction maps $\Pic(X)\to\Pic(Y(p))$, where $Y(p)$…

Given a directed graph D = (N, A) and a sequence of positive integers 1 <= c_1 < c_2 < ... < c_m <= |N|, we consider those path and cycle polytopes that are defined as the convex hulls of simple paths and cycles of D of cardinality c_p for…

Let $A$ be an excellent two-dimensional normal local ring containing an algebraically closed field and let $X\to \mathrm{Spec} (A)$ be a resolution of singularity. We prove a theorem giving a condition under which the dimension of the…

We construct homology theories with coefficients in L-spectra on the category of ball complexes and we define products in this setting. We also obtain signatures of geometric situations in these homology groups and prove product formulae…

Let P be a parabolic subgroup of a semisimple complex Lie group G defined by a subset \Sigma of simple roots of G, and let E_\phi be a homogeneous vector bundle over the flag manifold G/P corresponding to a linear representation \phi of P.…