论文标题
在已解决的F理论模型中生成分隔点的交点产品的功能
Generating functions for intersection products of divisors in resolved F-theory models
论文作者
论文摘要
在1703.00905的方法的基础上，我们提出了一种有效的算法，用于借助符号计算工具计算一系列椭圆纤维中除数的拓扑交集数。我们策略的关键部分是将除数的交叉产品组织成简洁的分析生成功能，即Kähler类的指数。我们使用1703.00905的方法将此函数的推动力计算到椭圆纤维的底部。我们在随附的Mathematica套件IntersectionNumbers.m中实现算法，该算法计算了与在任意复数维度的平滑基础上定义的F理论TATE模型分辨率的相交产品的生成功能。与先前探索的方法在1703.00905中的实现相比，我们的计算时间所需的计算时间显着减少了。作为例证，我们明确地计算了所有F理论模型的生成函数，这些模型具有简单的等级组，最多二十个，并以组等级突出显示计算时间的增长。
Building on the approach of 1703.00905, we present an efficient algorithm for computing topological intersection numbers of divisors in a broad class of elliptic fibrations with the aid of a symbolic computing tool. A key part of our strategy is organizing the intersection products of divisors into a succinct analytic generating function, namely the exponential of the Kähler class. We use the methods of 1703.00905 to compute the pushforward of this function to the base of the elliptic fibration. We implement our algorithm in an accompanying Mathematica package IntersectionNumbers.m that computes generating functions of intersection products for resolutions of F-theory Tate models defined over smooth base of arbitrary complex dimension. Our algorithm appears to offer a significant reduction in computation time needed to compute intersection numbers as compared to previously explored implementations of the methods in 1703.00905; as an illustration, we explicitly compute the generating functions for all F-theory Tate models with simple classical groups of rank up to twenty and highlight the growth of the computation time with the rank of the group.
