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Semantic segmentation of point clouds, aiming to assign each point a semantic category, is critical to 3D scene understanding.Despite of significant advances in recent years, most of existing methods still suffer from either the object-level misclassification or the boundary-level ambiguity. In this paper, we present a robust semantic segmentation network by deeply exploring the geometry of point clouds, dubbed GeoSegNet. Our GeoSegNet consists of a multi-geometry based encoder and a boundary-guided decoder. In the encoder, we develop a new residual geometry module from multi-geometry perspectives to extract object-level features. In the decoder, we introduce a contrastive boundary learning module to enhance the geometric representation of boundary points. Benefiting from the geometric encoder-decoder modeling, our GeoSegNet can infer the segmentation of objects effectively while making the intersections (boundaries) of two or more objects clear. Experiments show obvious improvements of our method over its competitors in terms of the overall segmentation accuracy and object boundary clearness. Code is available at https://github.com/Chen-yuiyui/GeoSegNet.