Mochizuki's indigenous bundles and Ehrhart polynomials |
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Authors: | Fu Liu Brian Osserman |
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Institution: | (1) Massachusetts Institute of Technology, Massachusetts;(2) University of California, Berkeley |
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Abstract: | 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.
The second author was supported by a fellowship from the Japan Society for the Promotion of Science during the preparation
of this paper. |
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Keywords: | Mochizuki Indigenous bundles Ehrhart polynomials Identities |
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