Mochizuki’s indigenous bundles and Ehrhart polynomials

Mochizuki’s work on torally indigenous bundles [1] yields combinatorial identities by degenerating to different curves of the same genus. We rephrase these identities in combinatorial language and strengthen them, giving relations between Ehrhart quasi-polynomials of different polytopes. We then apply the theory of Ehrhart quasi-polynomials to conclude that the number of dormant torally indigenous bundles on a general curve of a given type is expressed as a polynomial in the characteristic of the base field. In particular, we conclude the same for the number vector bundles of rank two and trivial determinant whose Frobenius-pullbacks are maximally unstable, as well as self-maps of the projective line with prescribed ramification.