A remark on 'Some numerical results in complex differential geometry'

In this note we verify certain statement about the operator $Q\_K$ constructed by Donaldson in [3] by using the full asymptotic expansion of Bergman kernel obtained in [2] and [4].Comment: 7 pages, modified the relation on $K\_p$ and $K\_{\omega,p}

Nucleon strangeness polarization from Λ/Λˉ\Lambda/\bar\Lambda hyperon production in polarized proton-proton collision at RHIC

We calculate the inclusive production of a polarized $\Lambda$ or $\bar{\Lambda}$ hyperon from the single longitudinally polarized proton and proton ($pp$) collision at RHIC. By comparing the data reported by the STAR Collaboration, we find that this process is sensitive to the polarization of strange and antistrange quarks of the proton in the experimental range. By introducing asymmetric coefficients with the minimization of $\chi^2$, we further identify the asymmetry of the polarized strange-antistrange quarks in the proton sea and find that the first moment is $\Delta s \approx -0.025\pm 0.019$ for strange quark and $\Delta\bar s \approx -0.001\pm 0.012$ for antistrange quark, with central values agreeing with the light-cone meson-baryon fluctuation model prediction, the recent lattice QCD determination of strangeness polarization and results from a global QCD analysis given by the Jefferson Lab Angular Momentum (JAM) Collaboration.Comment: 10 latex pages, 6 figures, final version for publicatio

Elliptic genus and vertex operator algebras

We construct bundles of modules of vertex operator algebras, and prove the rigidity and vanishing theorem for the Dirac operator on loop space twisted by such bundles. This result generalizes many previous results.Comment: 24 pages, Corrected typo

On the asymptotic expansion of Bergman kernel

We study the asymptotic of the Bergman kernel of the spin$^c$ Dirac operator on high tensor powers of a line bundle.Comment: Final version, 35 pages, J. Differential Geom. to appea

A remark on weighted Bergman kernels on orbifolds

In this note, we explain that Ross-Thomas' result on the weighted Bergman kernels on orbifolds can be directly deduced from our previous result. This result plays an important role in the companion paper to prove an orbifold version of Donaldson Theorem