Connections on Modules over Quasi-homogeneous Plane Curves
نویسنده
چکیده
Let k be an algebraically closed field of characteristic 0, and let A = k[x, y]/(f) be a quasi-homogeneous plane curve. We show that for any graded torsion free A-module M without free summands, there exists a natural graded integrable connection, i.e. a graded A-linear homomorphism ∇ : Derk(A) → Endk(M) that satisfy the derivation property and preserves the Lie product. In particular, a torsion free module N over the complete local ring B = Â admits a natural integrable connection if A is a simple curve singularity, or if A is irreducible and N is a gradable module.
منابع مشابه
2 00 6 Algebraic computation of some intersection D - modules
Let X be a complex analytic manifold, D ⊂ X a locally quasi-homogeneous free divisor, E an integrable logarithmic connection with respect to D and L the local system of the horizontal sections of E on X − D. In this paper we give an algebraic description in terms of E of the regular holonomic DX-module whose de Rham complex is the intersection complex associated with L. As an application, we pe...
متن کاملOn quasi-baer modules
Let $R$ be a ring, $sigma$ be an endomorphism of $R$ and $M_R$ be a $sigma$-rigid module. A module $M_R$ is called quasi-Baer if the right annihilator of a principal submodule of $R$ is generated by an idempotent. It is shown that an $R$-module $M_R$ is a quasi-Baer module if and only if $M[[x]]$ is a quasi-Baer module over the skew power series ring $R[[x,sigma]]$.
متن کاملQuasi-Primary Decomposition in Modules Over Proufer Domains
In this paper we investigate decompositions of submodules in modules over a Proufer domain into intersections of quasi-primary and classical quasi-primary submodules. In particular, existence and uniqueness of quasi-primary decompositions in modules over a Proufer domain of finite character are proved. Proufer domain; primary submodule; quasi-primary submodule; classical quasi-primary; decompo...
متن کاملAnalysis of Plane Waves in Anisotropic Magneto-Piezothermoelastic Diffusive Body with Fractional Order Derivative
In this paper the propagation of harmonic plane waves in a homogeneous anisotropic magneto-piezothermoelastic diffusive body with fractional order derivative is studied. The governing equations for a homogeneous transversely isotropic body in the context of the theory of thermoelasticity with diffusion given by Sherief et al. [1] are considered as a special case. It is found that three types of...
متن کاملA scheme over quasi-prime spectrum of modules
The notions of quasi-prime submodules and developed Zariski topology was introduced by the present authors in cite{ah10}. In this paper we use these notions to define a scheme. For an $R$-module $M$, let $X:={Qin qSpec(M) mid (Q:_R M)inSpec(R)}$. It is proved that $(X, mathcal{O}_X)$ is a locally ringed space. We study the morphism of locally ringed spaces induced by $R$-homomorphism $Mrightar...
متن کامل