Matematica per l'archeologia: ricostruire i pavimenti dai frammenti in loco

We present the complete reconstruction of the original aspect of the floors of the "tabernae" in the emicycle of the Trajan Markets in Rome, starting from the fragments on site. The complete analysis documentation for each of the 11 floors is contained in the essay. The reconstruction is univoquely obtained, thanks to a theorem of algebraic geometry of the 20th century. No integral recontruction of these floors is known, probably due to the fact that surviving fragments are often small and distant from each other. The algebraic-geometrical approach structures on situ information on a compositional level, and succeeds in reconstructing the global information about the aspect starting from less local information than normally deemed necessary by scholars of restauration and archaeology.