论文标题
在算术希尔伯特 - 塞缪尔定理上：通过变形证明
On the arithmetic Hilbert-Samuel theorem : a proof by deformation
论文作者
论文摘要
我们通过使用经典的降低裁缝理论中的经典减少，这是一个新的证据，这是射线套管理论中的经典减少，这是投影空间的直接证明以及对某些数值不变的保存，称为算术希尔伯特不变的不变，通过对锥体的投影完成。这种结构在于变形理论和阿拉克洛夫几何形状的交集。它提供了在正常锥体的变形上的Hermitian线束的变形。
We give a new proof the arithmetic Hilbert-Samuel theorem by using classical reductions in the theory of coherent sheaves, a direct proof in the case of the projective space and the conservation of some numerical invariants, called arithmetic Hilbert invariants, through the deformation to the projective completion of the cone. This construction lies at the intersection of deformation theory and Arakelov geometry. It provides a deformation of a Hermitian line bundle over the deformation to the normal cone.
