论文标题
正交Shimura品种上的Codimension 2的特殊周期的锥
Cones of special cycles of codimension 2 on orthogonal Shimura varieties
论文作者
论文摘要
令$ x $成为与单型格子相关的正交的shimura品种。我们研究了Codimension 2的特殊周期$ x $的圆锥$ \ MATHCAL {C} _x $的多面性。我们表明，这种循环产生的射线会积聚到无限的许多射线上，后者产生了一个非平凡的锥体。我们还证明了这种积累锥是多面体的。证明依赖于Siegel模块化形式的傅立叶系数所满足的类似特性。我们表明，$ \ Mathcal {C} _x $的积累光是通过与$ x $的Hodge类相交的Heegner Divisors的组合生成的。由于累积光线的分类，我们在SageMath中实现了一种算法，以证明$ \ Mathcal {C} _X _x $在某些情况下的多面性。
Let $X$ be an orthogonal Shimura variety associated to a unimodular lattice. We investigate the polyhedrality of the cone $\mathcal{C}_X$ of special cycles of codimension 2 on $X$. We show that the rays generated by such cycles accumulate towards infinitely many rays, the latter generating a non-trivial cone. We also prove that such an accumulation cone is polyhedral. The proof relies on analogous properties satisfied by the cones of Fourier coefficients of Siegel modular forms. We show that the accumulation rays of $\mathcal{C}_X$ are generated by combinations of Heegner divisors intersected with the Hodge class of $X$. As a result of the classification of the accumulation rays, we implement an algorithm in SageMath to certify the polyhedrality of $\mathcal{C}_X$ in some cases.
