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arXiv · 2405.16779

Simple obstructions and cone reduction

F. Qu
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Abstract

Let $X$ be a Deligne-Mumford stack locally of finite type over an algebraically closed field $k$ of characteristic zero. We show that the intrinsic normal cone $C_X$ of $X$ is supported in the subcone $\mathbb{V}(\Omega_X[-1])$ ($h^1/h^0((\Omega^1_X)^\vee)$) of its intrinsic normal sheaf $N_X$. This leads to an alternative proof of cone reduction by cosections for $C_X$. We also discuss vanishing of simple obstructions under the Buchweitz-Flenner semiregularity map for sheaves.

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F. Qu. 2024-05-27. Simple obstructions and cone reduction. https://doi.org/10.1515/advgeom-2025-0005

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