For each pair of positive integers (k, r) such that k+1, r−1 are coprime, we introduce an ideal I(k,r) n of the ring of symmetric polynomials C[x1, · · ·, xn]Sn. The ideal I(k,r) n has a basis consisting of Jack polynomials with parameter = −(r−1)/(k + 1), and admits an action of a family of differential operators of Dunkl type including the positive half of the Virasoro algebra. The space I(k,2)n coincides with the space of all symmetric polynomials in n variables which vanish when k + 1 variables are set equal. The space I(2,r)n coincides with the space of correlation functions of an abelian current of a vertex operator algebra related to Virasoro minimal series (3, r + 2).
In a recent paper, the first two authors proved that the generating series of the Poincare polynomials of the quasihomogeneous Hilbert schemes of points in the plane has a simple decomposition in an infinite product. In this paper, we give a very short geometrical proof of that formula.
A manifold M is locally conformally Kähler (LCK), if it admits a Kähler covering with monodromy acting by holomorphic homotheties. For a compact connected group G acting on an LCK manifold by holomorphic automorphisms, an averaging procedure gives a G-invariant LCK metric. Suppose that S1 acts on an LCK manifold M by holomorphic isometries, and the lifting of this action to the Kähler cover is not isometric. We show that admits an automorphic Kähler potential, and hence (for dimℂ M > 2) the manifold M can be embedded to a Hopf manifold.
A locally conformally Khler (LCK) manifold is a complex manifold which admits a covering endowed with a Kähler metric with respect to which the covering group acts through homotheties. We show that the blow-up of a compact LCK manifold along a complex submanifold admits an LCK structure if and only if this submanifold is globally conformally Kähler. We also prove that a twistor space (of a compact four-manifold, a quaternion-Kähler manifold, or a Riemannian manifold) cannot admit an LCK metric, unless it is Kähler.
We show that the derived category of any singularity over a field of characteristic 0 can be embedded fully and faithfully into a smooth triangulated category that has a semiorthogonal decomposition with components equivalent to derived categories of smooth varieties. This provides a categorical resolution of the singularity.
Cesaro convergence of spherical averages is proven for measurepreserving actions of Markov semigroups and groups. Convergence in the mean is established for functions in Lp, 1 p < 1, and pointwise convergence for functions in L1. In particular, for measure-preserving actions of word hyperbolic groups (in the sense of Gromov) we obtain Cesaro convergence of spherical averages with respect to any symmetric set of generators.
In this article, we calculate the ring of unstable (possibly nonadditive) operations from algebraic Morava K-theory K(n)^∗ to Chow groups with ℤ_(p) -coefficients. More precisely, we prove that it is a formal power series ring on generators c_i:K(n)^∗→CH^i⊗ℤ_(p) , which satisfy a Cartan-type formula.
В статье чисто комбинаторным способом доказана топологическая рекурсия для задачи перечисления двухцветных карт (являющихся двойственными объектами к детским рисункам). Кроме этого, доказано уравнение квантовой спектральной кривой для данной задачи. Предложено обобщение вышеописанных результатов на случай четырехцветных карт.