The Global Sections of Chiral de Rham Complexes on Compact Ricci-Flat Kähler Manifolds

@article{Song2018TheGS,
  title={The Global Sections of Chiral de Rham Complexes on Compact Ricci-Flat K{\"a}hler Manifolds},
  author={Bailin Song},
  journal={arXiv: Quantum Algebra},
  year={2018}
}
  • Bailin Song
  • Published 27 September 2018
  • Physics, Mathematics
  • arXiv: Quantum Algebra
The space of the global sections of chiral de Rham complex on a compact Ricci-flat K\"ahler manifold is calculated and it is expressed as an invariant subspace of a $\beta\gamma-bc$ system under the action of certain Lie algebra. 
Chiral de Rham complex on the upper half plane and modular forms.
For any congruence subgroup $\Gamma$, we study the vertex operator algebra $\Omega^{ch}(\mathbb H,\Gamma)$ constructed from the $\Gamma$-invariant global sections of the chiral de Rham complex on theExpand
INVARIANT SUBALGEBRAS OF THE SMALL 𝒩 = 4 SUPERCONFORMAL ALGEBRA
Various aspects of orbifolds and cosets of the small $\mathcal{N}=4$ superconformal algebra are studied. First, we determine minimal strong generators for generic and specific levels. As a corollary,Expand
Standard monomials and invariant theory for arc spaces I: general linear group
Classical invariant theory. Classical invariant has a long history that began in the 19th century in work of Cayley, Gordan, Klein, and Hilbert. Given an algebraically closed field K, a reductiveExpand

References

SHOWING 1-10 OF 31 REFERENCES
The global sections of the chiral de Rham complex on a Kummer surface
The chiral de Rham complex is a sheaf of vertex algebras {\Omega}^ch_M on any nonsingular algebraic variety or complex manifold M, which contains the ordinary de Rham complex as the weight zeroExpand
Chiral de Rham Complex
Abstract:We define natural sheaves of vertex algebras over smooth manifolds which may be regarded as semi-infinite de Rham complexes of certain D-modules over the loop spaces. For Calabi–YauExpand
Supersymmetry of the chiral de Rham complex II: Commuting Sectors
We construct two commuting N=2 structures on the space of sections of the chiral de Rham complex (CDR) of a Calabi-Yau manifold. We use this extra supersymmetry to construct a non-linear automorphismExpand
EXTENSION OF N = 2 SUPERCONFORMAL ALGEBRA AND CALABI-YAU COMPACTIFICATION
We study an extension of N = 2 superconformal algebra by the addition of the spectral flow generators. We present the extended algebra corresponding to complex 3-dimensional Calabi-Yau manifold andExpand
Chiral de Rham complex and the half-twisted sigma-model
On any Calabi-Yau manifold X one can define a certain sheaf of chiral N=2 superconformal field theories, known as the chiral de Rham complex of X. It depends only on the complex structure of X, andExpand
Supersymmetry of the chiral de Rham complex
Abstract We present a superfield formulation of the chiral de Rham complex (CDR), as introduced by Malikov, Schechtman and Vaintrob in 1999, in the setting of a general smooth manifold, and use it toExpand
Chiral Poincaré duality
by fermionic number p and conformal weight i. The Z/2-grading is p (mod 2). The conformal weight zero part Ω 0 = ⊕p Ω 0 is identified with the usual de Rham algebra ΩX = ⊕p ΩpX of differential forms.Expand
Vector bundles induced from jet schemes
A family of holomorphic vector bundles is constructed on a complex manifold $X$. The space of the holomorphic sections of these bundles are calculated in certain cases. As an application, if $X$ isExpand
Chiral de Rham complex on the upper half plane and modular forms.
For any congruence subgroup $\Gamma$, we study the vertex operator algebra $\Omega^{ch}(\mathbb H,\Gamma)$ constructed from the $\Gamma$-invariant global sections of the chiral de Rham complex on theExpand
Compact Manifolds with Special Holonomy
The book starts with a thorough introduction to connections and holonomy groups, and to Riemannian, complex and Kahler geometry. Then the Calabi conjecture is proved and used to deduce the existenceExpand
...
1
2
3
4
...