Local feature matching is typically formulated for image pairs, although structure-from-motion and visual localization commonly match one reference image against many retrieved or covisible neighbours. Applying a pairwise matcher independently to these centre-neighbour edges duplicates reference-side computation and prevents the matcher from exploiting complementary multi-view geometric evidence from the remaining observations. To address these limitations, we introduce MVLoMa, a sparse star-graph matcher that extends LoMa from image pairs to multiple views. MVLoMa first uses a frozen multi-view geometry model to jointly describe all images in a star, then injects the resulting cross-view geometric context into local descriptors. It then matches the centre image to all neighbours in a single forward pass through per-view self-attention and bidirectional centre-neighbour cross-attention. For supervision, we derive positive correspondences only from depth-valid, mutually visible dense warps and explicitly penalize high-confidence matches that violate epipolar geometry. On 25-view star graphs from HyperSim, ScanNet++, Mip-NeRF 360, and Tanks and Temples, MVLoMa obtains the best macro-average relative-pose AUC among the compared methods at all three thresholds (58.65/85.41/90.99). Its matcher is 2.20 times faster than sequential evaluation of the 24 centre-neighbour edges. The same design supports four tested frozen geometry encoders -- DA3, $π^3$, VGGT, and VGGT-$Ω$ -- with DA3-Giant performing best on all reported encoder-ablation metrics. Controlled ablations further isolate the effects of geometry-aware descriptors, visibility filtering, geometric negative supervision, and joint multi-view inference.

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