What is the term for the awning that provided shade over the theatre or amphitheatre during summer?

The term for the awning that provided shade over the theatre or amphitheatre during summer is "velarium." This large, fabric awning was essential for creating a more comfortable environment for spectators during performances, shielding them from the harsh sunlight. The construction of the velarium involved a complex system of ropes and pulleys that allowed it to be deployed and retracted as needed, demonstrating the architectural ingenuity of the Romans.

In contrast, the other terms do not refer to the awning itself. "Ianconium" is not commonly recognized in this context. "Cavea" refers to the seating area in theatres or amphitheatres, and "sparsiones" relates to the practice of sprinkling water to cool the audience or enhance the effects of performances, rather than to the shading structure itself. Thus, "velarium" is the correct term that encapsulates the concept of providing shade in these ancient venues.