About the arithmetic volume on smooth ring patterns

作者：Hajli Mounir^*

来源：Kyoto Journal of Mathematics, 2014, 54(4): 819-840.

DOI：10.1215/21562261-2801831

Let X be a smooth projective toric scheme over Spec(Z). Let (D) over bar be an equivariant line bundle on X, endowed with a continuous Hermitian metric which is invariant by the action of the compact torus of X(C). We show that its arithmetic volume is given in terms of the Legendre-Fenchel transform associated to the metric. When (D) over bar is supposed admissible, we characterize when it is arithmetically ample, nef, or big in terms of combinatorial date.

• 出版日期2014