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Over an algebraically closed field of characteristic $p>2$, the 0-dimensional and 1-dimensional cohomology of the queer Lie superalgebra $\frak{q}(2)$ with coefficients in all baby Verma modules and all the simple modules are determined.
We describe a class of integrable models of 1+1 and 1-dimensional dilaton gravity coupled to scalar fields. The models can be derived from high dimensional supergravity theories by dimensional reductions. The equations of motion of these…
A presentation of a degree $d$ form in $n+1$ variables as the sum of homogenous elements ``essentially'' involving $n$ variables is called a {\em codimension one decomposition}. Codimension one decompositions are introduced and the related…
A linear constraint is given on the Betti numbers of a compact hyper-Kaehler manifold, using an index formula for c_1c_{n-1} on an almost complex manifold. The topology of some other manifolds with reduced holonomy is also discussed…
We extend a recent result on the existence of wandering domains of polynomial functions defined over the p-adic field C_p to any algebraically closed complete non-archimedean field C_K with residue characteristic p>0. We also prove that…
This first part of the paper describes the support of top graded local cohomology modules. As a corrolary one obtains a simple criteria for the vanishing of these modules and also the fact that they have finitely many minimal primes. The…
Let $p$ be a prime and let $\mathbb{Q}_p$ be the field of $p$-adic numbers. It is known that the finite extensions of $\mathbb{Q}_p$ of a given degree are finite up to isomorphism. Given a cubic field extension $L$ of $\mathbb{Q}_p$…
This article studies germs of holomorphic vector fields at the origin of C3 that are tangent to holomorphic foliations of codimension one. Two situations are considered. First, we assume hypotheses on the reduction of singularities of the…
We consider the question "Is every nonzero generic degree a density-1-bounding generic degree?" By previous results \cite{I2} either resolution of this question would answer an open question concerning the structure of the generic degrees:…
We construct field theories in $2+1$ dimensions with multiple conformal symmetries acting on only one of the spatial directions. These can be considered a conformal extension to "subsystem scale invariances", borrowing the language often…
We investigate the weak gravity bounds on the U(1) gauge theory and scalar field theories in various dimensional noncommutative space. Many results are obtained, such as the upper bound on the noncommutative scale $g_{YM}M_p$ for four…
We prove that a smooth scheme of dimension $n$ over a perfect field is A^1-weakly equivalent to a point if it is A^1-n-connected. We also prove an excision result for A^1-homotopy sheaves over a perfect field.
We demonstrate counterexamples to Wilmshurst's conjecture on the valence of harmonic polynomials in the plane, and we conjecture a bound that is linear in the analytic degree for each fixed anti-analytic degree. Then we initiate a…
The spline space $C_k^r(\Delta)$ attached to a subdivided domain $\Delta$ of $\R^{d} $ is the vector space of functions of class $C^{r}$ which are polynomials of degree $\le k$ on each piece of this subdivision. Classical splines on planar…
This paper investigates the relationship between the solvability of first-order differential equations and the topology of the underlying domain through the lens of de\,Rham cohomology. We analyze the conditions under which a closed 1-form…
Recently, Corvaja and Zannier obtained an extension of the Subspace Theorem with arbitrary homogeneous polynomials of arbitrary degreee instead of linear forms. Their result states that the set of solutions in P^n(K) (K number field) of the…
In recent decades, the defect of finite extensions of valued fields has emerged as the main obstacle in several fundamental problems in algebraic geometry such as the local uniformization problem. Hence, it is important to identify…
This article studies the set of R-equivalence classes of the group of proper projective similitudes of an algebra with involution of the first kind. The main results concern base fields of characteristic different from 2 over which every…
We prove the Tate conjecture for divisor classes and the Mumford-Tate conjecture for the cohomology in degree 2 for varieties with $h^{2,0}=1$ over a finitely generated field of characteristic 0, under a mild assumption on their moduli. As…
We present the results of computation of cohomology for some Lie (super)algebras of Hamiltonian vector fields and related algebras. At present, the full cohomology rings for these algebras are not known even for the low dimensional vector…