Let Z=m_1P_1+⋯ +m_sP_s be a set of fat points in ℙ^n . Let ϕ be a linear embedding of ℙ^n in ℙ^m, n
For a compact connected Lie group G, the rational cohomology ring of its classifying space BG can be expressed as an invariant ring. Namely, for a maximal torus T^n of G, it is well–known that H^*(BG; ℚ ) ≅ H^*(BT^n; ℚ )^W(G) which is a polynomial ring. If d divides n, the quotient SU(n)/ℤ_d is also a Lie group. Their rational cohomology rings are isomorphic, however, the integral representations of the Weyl groups W(SU(n)/ℤ_d) are not equivalent. So we ask if the modular invariant rings under the actions are polynomial. Our main theorem is a generalization of some results in [4] and [12].
In this paper, we provide a new property for the Smoluchowski-Kramers approximation of stochastic differential equations. We prove the convergence of the derivative of solutions with respect to the initial condition (when the mass of particles tends to zero). We then use the techniques of Malliavin calculus to obtain an explicit Berry-Esseen error bound for the rate of convergence.
In this paper, we establish a non-effective version of Schmidt’s subspace theorem for moving hypersurface targets in weak general position on algebraic varieties over function fields.
This paper deals with certain classes of modules under module-finite extensions. Let φ : R↪ S be a module-finite extension between commutative Noetherian local rings. We investigate the transfer of Artinian module structures and attached primes between R and S. We clarify the behavior of local cohomology modules as well as certain structures of finitely generated S-modules under the restriction of scalars to R via φ . We show that R is a quotient of a Cohen-Macaulay local ring if and only if so is S. As an application, we characterize the structure of Nagata’s idealization. Using Macaulayfication of algebraic varieties and idealization, we give an example to illustrate the results.
