Hilbert-Samuel formula over adelic curves

去年我证明了一个相对的Siu不等式，利用它我们重新证明了函数域上的等长线丛的等分布定理，在此之后，今年我想把等分布定理推广到线丛恰好很大的情况。在“斜率有界性与等分布定理”一文中，我们讨论了Hilbert-Samuel公式、极小斜率有界性与等分布定理之间的相互关系。在本文的最后，我们研究了椭圆曲线上半样本锥的卡体积的性质。证明了半充分半正的阿德利克线丛的一个希尔伯特-塞缪尔公式。

Last year, I proved a relative version of Siu's inequality, by which we provide a reproof of Equidistribution theorem with respect to an adelic ample line bundle over a function field.After that work, this year I want to extend the equidistribution theorem to case that the line bundle is just big. In the paper "Slope boundedness and equidistribution theorem", we discussed the interplay between HIlbert-Samuel formulas, boundedness of minimal slopes, and equidistribution theorem. I successively proved those results holds for any adelic big line bundles over any global field of characteristic 0.In the end of the project, I studied the behavior of chi-volume on the semiample cone over an adelic curve. I proved a Hilbert-Samuel formula for a semiample and semipositive adelic line bundle.