For an affine toric variety we give a convex geometric description of the Hodge decomposition of its Hochschild cohomology. Moreover, we show that every Poisson structure on a possibly singular affine toric variety can be quantized in the sense of deformation quantization.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/3207