Real Gromov–Witten theory in all genera and real enumerative geometry: Properties
Real Gromov–Witten theory in all genera and real enumerative geometry: Properties
复制标题
所有属中的真实格罗莫夫-维滕理论和真实枚举几何：属性
DOI：
10.4310/jsg.2019.v17.n4.a5
复制
发表时间：
2015
影响因子：
0.7
通讯作者：
A. Zinger
中科院分区：
文献类型：
--
作者：
Penka V. Georgieva;A. Zinger
这项工作的第一部分构造了奇“复”维实可定向辛流形的正亏格实Gromov-Witten不变量；本部分重点讨论了它们的性质，这些性质对于实际使用这些不变量是必不可少的。我们确定了第一部分中构造的实映射的模空间上的方向与Gromov-Witten的标准节点识别浸入理论的相容。我们还将这些定向与在特殊情况下可用的对实映射的模空间定向的其他方法进行了比较。在续篇中，我们利用所建立的性质比较了实Gromov-Witten不变量和计数不变量，描述了计算奇维射影空间的实Gromov-Witten不变量的等变局部化数据，并在Walcher预言的精神下建立了这些不变量的消失结果。
The first part of this work constructs positive-genus real Gromov-Witten invariants of real-orientable symplectic manifolds of odd "complex" dimensions; the present part focuses on their properties that are essential for actually working with these invariants. We determine the compatibility of the orientations on the moduli spaces of real maps constructed in the first part with the standard node-identifying immersion of Gromov-Witten theory. We also compare these orientations with alternative ways of orienting the moduli spaces of real maps that are available in special cases. In a sequel, we use the properties established in this paper to compare real Gromov-Witten and enumerative invariants, to describe equivariant localization data that computes the real Gromov-Witten invariants of odd-dimensional projective spaces, and to establish vanishing results for these invariants in the spirit of Walcher's predictions.