论文标题
对数Gromov-witten理论和双重影响周期
Logarithmic Gromov-Witten theory and double ramification cycles
论文作者
论文摘要
我们研究了相对于其完整的感谢您的圆环边界的对数Gromov-witten周期。这些周期表示为曲线模量空间的对数圆环中的双重分支周期和天然重言式类别的产物。我们引入了一种简单的新技术，该技术将刚性和橡胶几何形状的格罗莫夫（Gromov）编织周期介绍。该技术基于对对数代数圆环的地图的研究。通过将其与对数的双重影响周期的最新作品相结合，我们推断出所有对数Gromov-Witten Pushforwards，用于与其完整的感谢您的整个曲线边界相对于曲折的多样性的地图，位于曲线模仿空间的重言式环中。该方法的一个特征是，它避免了尚未开发的对数虚拟定位公式，而是直接依靠分段多项式函数来捕获该公式将提供的结构。结果给出了Faber-Pandharipande的工作，以及Holmes-Schwarz和Molcho-Ranganathan的最新工作。证明通过一般结构在稳定地图的空间上传递到对数代数圆环的空间，这可能是独立的。
We examine the logarithmic Gromov-Witten cycles of a toric variety relative to its full toric boundary. The cycles are expressed as products of double ramification cycles and natural tautological classes in the logarithmic Chow ring of the moduli space of curves. We introduce a simple new technique that relates the Gromov-Witten cycles of rigid and rubber geometries; the technique is based on a study of maps to the logarithmic algebraic torus. By combining this with recent work on logarithmic double ramification cycles, we deduce that all logarithmic Gromov-Witten pushforwards, for maps to a toric variety relative to its full toric boundary, lie in the tautological ring of the moduli space of curves. A feature of the approach is that it avoids the as yet undeveloped logarithmic virtual localization formula, instead relying directly on piecewise polynomial functions to capture the structure that would be provided by such a formula. The results give a common generalization of work of Faber-Pandharipande, and more recent work of Holmes-Schwarz and Molcho-Ranganathan. The proof passes through general structure results on the space of stable maps to the logarithmic algebraic torus, which may be of independent interest.
