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arXiv · 1706.00580

Hochschild Cohomology and Deformation Quantization of Affine Toric Varieties

Matej Filip
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Abstract

For an affine toric variety $\mathrm{Spec}(A)$, we give a convex geometric description of the Hodge decomposition of its Hochschild cohomology. Under certain assumptions we compute the dimensions of the Hodge summands $T^1_{(i)}(A)$, generalizing the existing results about the Andre-Quillen cohomology group $T^1_{(1)}(A)$. We prove that every Poisson structure on a possibly singular affine toric variety can be quantized in the sense of deformation quantization.

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Matej Filip. 2017-06-02. Hochschild Cohomology and Deformation Quantization of Affine Toric Varieties. https://arxiv.org/abs/1706.00580

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