论文标题
精制复曲面的计算II
Computation of refined toric invariants II
论文作者
论文摘要
2015年，G。〜Mikhalkin提出了精致的曲折表面中理性曲线的精致计数。计数曲线必须穿过位于表面曲折边界上的一些真实和复杂点，并且根据所谓的量子指数的值进行了完善。这种计数仅取决于每个感谢您的分隔的复杂点的数量，从而导致不变。首先，我们提供了一种计算任何方向的实际理性曲线的量子索引，从而摆脱了复杂点上先前需要的“纯粹虚构”假设。然后，我们使用热带几何方法将这些经典的精制不变性与热带精制不变性相关联，该方法使用Block-Göttsche多重性定义。这概括了Mikhalkin在所有点都是真实的情况下与两个不变的结果相关的结果，以及作者的结果，即复杂点位于单个圆磨分裂上。
In 2015, G.~Mikhalkin introduced a refined count for real rational curves in toric surfaces. The counted curves have to pass through some real and complex points located on the toric boundary of the surface, and the count is refined according to the value of a so called quantum index. This count happens only to depend on the number of complex points on each toric divisors, leading to an invariant. First, we give a way to compute the quantum index of any oriented real rational curve, getting rid of the previously needed "purely imaginary" assumption on the complex points. Then, we use the tropical geometry approach to relate these classical refined invariants to tropical refined invariants, defined using Block-Göttsche multiplicity. This generalizes the result of Mikhalkin relating both invariants in the case where all the points are real, and the result of the author where complex points are located on a single toric divisor.
