Polyvector fields for Fano 3-folds
Pieter Belmans, Enrico Fatighenti, Fabio Tanturri
TL;DR
This paper computes the Hochschild-Kostant-Rosenberg decomposition of Hochschild cohomology for Fano 3-folds, providing initial insights into their Poisson structures and Gerstenhaber algebra, aiding classification efforts.
Contribution
It is the first to analyze the Hochschild-Kostant-Rosenberg decomposition for Fano 3-folds, advancing understanding of their algebraic structures.
Findings
Hochschild-Kostant-Rosenberg decomposition computed for Fano 3-folds
Initial insights into Gerstenhaber algebra structure
Implications for classifying Poisson structures
Abstract
We compute the Hochschild-Kostant-Rosenberg decomposition of the Hochschild cohomology of Fano 3-folds. This is the first step in understanding the non-trivial Gerstenhaber algebra structure, and yields some initial insights in the classification of Poisson structures on Fano 3-folds of higher Picard rank.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology