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In the context of distributed certification, the recognition of graph classeshas started to be intensively studied. For instance, different results relatedto the recognition of planar, bounded tree-width and $H$-minor free graphs havebeen recently obtained. The goal of the present work is to design compactcertificates for the local recognition of relevant geometric intersection graphclasses, namely interval, chordal, circular arc, trapezoid and permutation.More precisely, we give proof labeling schemes recognizing each of theseclasses with logarithmic-sized certificates. We also provide tight logarithmiclower bounds on the size of the certificates on the proof labeling schemes forthe recognition of any of the aforementioned geometric intersection graphclasses.

Local Certification of Some Geometric Intersection Graph Classes