标题： 在theta映射下的码多项式的像 显示英文标题

标题： On the image of code polynomials under theta map

摘要： theta映射将码多项式映射到偶数权的西格尔模形式环中。 对于$g\leq 3$，图像的显式描述已知，且theta映射的满射性随之得出。 相反，已知对于$g\geq 5$，该映射不是满射的。 在本文中，我们讨论相关射影簇之间的嵌入可能性。 我们证明对于$g\geq 4$，这是不可能的，因此我们得到了剩余情况$g=4$的分次环的非满射性。 显示英文摘要

摘要： The theta map sends code polynomials into the ring of Siegel modular forms of even weights. Explicit description of the image is known for $g\leq 3$ and the surjectivity of the theta map follows. Instead it is known that this map is not surjective for $g\geq 5$. In this paper we discuss the possibility of an embedding between the associated projective varieties. We prove that this is not possible for $g\geq 4$ and consequently we get the non surjectivity of the graded rings for the remaining case $g=4$.