论文标题
椭圆属的刚度：从数字理论到几何和背部
Rigidity of elliptic genera: from number theory to geometry and back
论文作者
论文摘要
在本文中，我们得出了椭圆属刚性的拓扑和数量理论后果，它们是与每个紧凑型几乎复杂的歧管相关的特殊模块化形式。特别是，在几何侧，我们证明刚性意味着贝蒂数与尺寸紧凑的符号歧管的索引之间的关系，$ 2N $承认具有隔离固定点的圆圈的哈密顿动作。我们研究了最大索引和复曲面作用的情况。在数量的理论方面，我们证明，从每个紧凑的索引几乎复杂的歧管大于一个的复杂歧管，可以赋予一个具有孤立固定点的圆的作用，可以在Eisenstein系列中得出非平凡的关系。我们给出了来自$ \ mathbb {c} p^n $的标准操作的明确公式。
In this paper we derive topological and number theoretical consequences of the rigidity of elliptic genera, which are special modular forms associated to each compact almost complex manifold. In particular, on the geometry side, we prove that rigidity implies relations between the Betti numbers and the index of a compact symplectic manifold of dimension $2n$ admitting a Hamiltonian action of a circle with isolated fixed points. We investigate the case of maximal index and toric actions. On the number theoretical side we prove that from each compact almost complex manifold of index greater than one, that can be endowed with the action of a circle with isolated fixed points, one can derive non-trivial relations among Eisenstein series. We give explicit formulas coming from the standard action on $\mathbb{C} P^n$.
