Mochizuki's indigenous bundles and Ehrhart polynomials
Mochizuki's indigenous bundles and Ehrhart polynomials
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DOI：
10.1007/s10801-006-6920-x
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发表时间：
2006-03-01
影响因子：
0.8
通讯作者：
Osserman, B
中科院分区：
文献类型：
--
作者：
Liu, F;Osserman, B
Mochizuki对torally土著丛[1]的工作通过退化到同一亏格的不同曲线而产生组合恒等式。我们改写这些身份组合的语言，并加强他们，Ehrhart准多项式不同的多面体之间的关系。然后，我们应用Ehrhart准多项式的理论得出结论，休眠torally土著丛的数量在一个给定类型的一般曲线表示为多项式的特征的基字段。特别是，我们得出同样的结论的秩2和平凡行列式的Frobenius拉回是最大不稳定的，以及自映射的规定的分歧的投射线。
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.