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arXiv · 2605.04529

Stability conditions and infinitesimal deformation of curves

Kotaro Kawatani
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Abstract

Let $\mathcal X$ be an infinitesimal deformation of a smooth projective curve $X_0$ over a field. We study stability conditions under such deformations and show that the derived push-forward functor associated with the inclusion $X_0 \to \mathcal X$ induces an isomorphism between the space of stability conditions on $\mathcal X$ and that on $X_0$. This yields a direct comparison between the deformed and undeformed settings. As an application, we prove that the autoequivalence group $\mathrm{Aut}{\mathbf D^b(\mathcal X)}$ naturally acts on $\mathbf D^b(X_0)$, providing a link between derived symmetries and the deformation structure.

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Kotaro Kawatani. 2026-05-06. Stability conditions and infinitesimal deformation of curves. https://arxiv.org/abs/2605.04529

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