论文标题
Siegel-Jacobi形式的界面相对索引的环没有有限生成
Rings of Siegel-Jacobi forms of bounded relative index are not finitely generated
论文作者
论文摘要
我们表明，固定程度的Siegel-Jacobi形式的环以及重量和索引之间的固定或界比的环没有有限地产生。我们的主要工具是环形b划分的理论及其与凸几何的关系。作为我们方法的副产品，我们证明了Kramer的猜想是关于所有Siegel-Jacobi形式的表示为某些线捆绑包的部分，并且由于TAI而导致的公式用于siegel-jacobi的渐近维度，而重量和索引之间给定比率的比率。
We show that the ring of Siegel-Jacobi forms of fixed degree and of fixed or bounded ratio between weight and index is not finitely generated. Our main tool is the theory of toroidal b-divisors and their relation to convex geometry. As a byproduct of our methods, we prove a conjecture of Kramer about the representation of all Siegel-Jacobi forms as sections of certain line bundles and we recover a formula due to Tai for the asymptotic dimension of the space of Siegel-Jacobi forms of given ratio between weight and index.
