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arXiv · 2505.04023

NC-smooth thickenings and Jacobians

Alexander Polishchuk
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Abstract

We prove that a bounded complex of coherent sheaves on an abelian variety A, whose Fourier-Mukai transform has support of dimension at most 1, extends to a perfect complex on the standard NC-smooth thickening of A and on the deformation quantization of any constant Poisson bracket on A. We discuss a related conjectural characterization of Jacobians in terms of NC-smooth thickenings.

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Alexander Polishchuk. 2025-05-06. NC-smooth thickenings and Jacobians. https://arxiv.org/abs/2505.04023

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