Geodesic
Mochizuki's indigenous bundles and Ehrhart polynomials
Journal of Algebraic Combinatorics, Tome 23 (2006) no. 2, pp. 125-136.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Mots-clés : keywords mochizuki, indigenous bundles, Ehrhart polynomials, identities 
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     title = {Mochizuki's indigenous bundles and {Ehrhart} polynomials},
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     language = {en},
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Liu, Fu; Osserman, Brian. Mochizuki's indigenous bundles and Ehrhart polynomials. Journal of Algebraic Combinatorics, Tome 23 (2006) no. 2, pp. 125-136. https://geodesic-test.mathdoc.fr/item/JAC_2006__23_2_a4/