Sheaf lines of Yang-Mills Instanton Sheaves

Yang-Mills Instanton Sheaves

The SL(2,C) Yang-Mills instanton solutions constructed recently by the biquaternion method were shown to satisfy the complex version of the ADHM equations and the Monad construction. Moreover, we discover that, in addition to the holomorphic vector bundles on CP^3 similar to the case of SU(2) ADHM construction, the SL(2,C) instanton solutions can be used to explicitly construct instanton sheaves on CP^3. Presumably, the existence of these instanton sheaves is related to the singularities of the SL(2,C) instantons on S^4 which do not exist for SU(2) instantons.

Yang-Mills Instanton Sheaves with Higher Topological Charges

We explicitly construct SL(2,C) Yang-Mills (weakly) three and four instanton sheaves on CP^3. These results extend the previous construction of Yang-Mills (weakly) instanton sheaves with topological charge two [18].

Lectures on perverse sheaves on instanton moduli spaces

I will explain my joint paper `Instantons moduli spaces and W-algebras' with A.Braverman, M.Finkelberg, arXiv:1406.2381. I will concentrate on the geometric part, that is a study of perverse sheaves on instanton moduli spaces. I place a particular emphasize on the hyperbolic restriction functor and stable envelop, which are our key tools, and appear also in other situations in geometric representation theory. These are lecture notes for a course in 2015 PCMI.

Extended Complex Yang-Mills Instanton Sheaves

In the search of YM instanton sheaves with topological charge two, the rank of beta matrix in the monad construction can be dropped from the bundle case with rank(beta)= 2 to either rank(beta) = 1 [4] or 0 on some points of CP^3 of the sheaf cases. In this paper, we first show that the sheaf case with rank(beta)= 0 does not exist for the previous construction of SU(2) complex YM instantons [3]. We then show that in the new "extended complex YM instantons" discovered in this paper, rank(beta) can be either 2 on the whole CP^3 (bundle) with some given ADHM data or 1, 0 on some points of CP^3 wit…

Bargmann-Fock sheaves on Kähler manifolds

Fedosov used flat sections of the Weyl bundle on a symplectic manifold to construct a star product $\star$ which gives rise to a deformation quantization. By extending Fedosov's method, we give an explicit, analytic construction of a sheaf of Bargmann-Fock modules over the Weyl bundle of a Kähler manifold $X$ equipped with a compatible Fedosov abelian connection, and show that the sheaf of flat sections forms a module sheaf over the sheaf of deformation quantization algebras defined $(C^\infty_X[[\hbar]], \star)$. This sheaf can be viewed as the $\hbar$-expansion of $L^{\otimes k}$ as $k \to \…

Poisson流形上N=2超对称顶点代数的层

Sheaves of N=2 supersymmetric vertex algebras on Poisson manifolds

我们构造了一个N=2的顶点代数层，它自然地与任何Poisson流形相关联。这层的手征的德拉姆复杂的关系进行了讨论。我们重新证明了关于在Calabi-Yau流形的手征de Rham复形的截面空间上存在两个可交换的N = 2超共形结构的结果，但现在是在一个明显的N=2形式主义中计算的。讨论了N=2顶点代数层的半经典极限与经典超对称非线性西格玛模型的关系。