The Gerstenhaber product HH2(A)×HH2(A)→HH3(A) of affine toric varieties

Abstract

For an affine toric variety $\text{Spec}(A)$, we give a convex geometric interpretation of the Gerstenhaber product ${\text{HH}}^2(A)\times {\text{HH}}^2(A)\to {\text{HH}}^3(A)$ between the Hochschild cohomology groups. In particular, our construction also generalizes the known results about the cup product $T_A^1\times T_A^1\to T_A^2$.

Keywords:

• Gerstenhaber product
• Harrison cohomology
• Hochschild cohomology
• toric varieties

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 13D03
• 13D10
• 14B05
• 14B07
• 14M25

Acknowledgements

I would like to thank to my PhD advisor Klaus Altmann, for his constant support and for providing clear answers to my many questions. I am also grateful to Arne B. Sletsjøe for useful discussions.