Achieving dexterous grasping remains a key challenge in robotics. Recent generative approaches enable diverse grasps through large-scale data-driven training, yet they often neglect geometric priors of objects, which leads to low data efficiency and poor physical plausibility. We propose GeoDexGrasp, a geometry-aware generation framework for dexterous grasping built upon object-centric geometric representations. We introduce a SIM(3)-equivariant network equipped with a self-supervised disentanglement strategy to extract interpretable and transferable geometric features, including shape, size, pose, and interaction direction. The overall generation process is then decomposed into two stages: first, root rotation generation conditioned on pose and interaction direction; second, hand grasp generation guided by shape and size. By leveraging geometric representations, GeoDexGrasp achieves state-of-the-art physical plausibility (reducing 40% penetration depth) across five datasets and exhibits improved data efficiency. Additionally, GeoDexGrasp is lightweight, using less than 20% of the parameters of the previous state-of-the-art method, while attaining a comparable grasp success rate.
