Year: 2026
Type: preprint
Abstract: Inspired by Mukai's work on K3 surfaces, we introduce and study a notion of semi-rigidity for stable sheaves on smooth polarised varieties, designed to capture the existence of stable deformations of direct sums. We show that semi-rigidity is detected by the absence of decomposable elements in the kernel of the Yoneda pairing. We apply the resulting criterion to line bundles on smooth projective varieties and to line bundles supported on smooth Lagrangian subvarieties of hyper-Kähler manifolds.
Source: arXiv (Cornell University)
Authors: Bottini, Alessio, Carini, Riccardo
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7134884496
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