The first part of this work constructs real positive-genus Gromov-Witten invariants of real-orientable symplectic manifolds of odd "complex" dimensions; the second part studies the orientations on the moduli spaces of real maps used in constructing these invariants. The present paper applies the results of the latter to obtain quantitative and qualitative conclusions about the invariants defined in the former. After describing large collections of real-orientable symplectic manifolds, we show that the real genus 1 Gromov-Witten invariants of sufficiently positive almost Kahler threefolds are signed counts of real genus 1 curves only and thus provide direct lower bounds for the counts of these curves in such targets. We specify real orientations on the real-orientable complete intersections in projective spaces; the real Gromov-Witten invariants they determine are in a sense canonically determined by the complete intersection itself, (at least) in most cases. We also obtain equivariant localization data that computes the real invariants of projective spaces and determines the contributions from many torus fixed loci for other complete intersections. Our results confirm Walcher's predictions for the vanishing of these invariants in certain cases and for the localization data in other cases.

中文翻译：

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所有属和实枚举几何中的实格罗莫夫-维滕理论：计算

这项工作的第一部分构造了奇“复”维数的可实向辛流形的实正属 Gromov-Witten 不变量；第二部分研究用于构造这些不变量的实映射模空间的方向。本文应用后者的结果来获得关于前者定义的不变量的定量和定性结论。在描述了大量实数可定向辛流形之后，我们证明了足够正的几乎 Kahler 三重的实属 1 Gromov-Witten 不变量只是实属 1 曲线的有符号计数，因此为这些曲线的计数提供了直接下界这样的目标。我们在射影空间中的可实向完全交集上指定实向；他们确定的真正的 Gromov-Witten 不变量在某种意义上是由完整的交集本身规范确定的，（至少）在大多数情况下。我们还获得了等变定位数据，该数据计算了投影空间的真实不变量，并确定了许多环面固定位点对其他完整交叉点的贡献。我们的结果证实了 Walcher 对某些情况下这些不变量消失的预测以及其他情况下定位数据的预测。