论文标题
较高维的热带顶点
The Higher Dimensional Tropical Vertex
论文作者
论文摘要
我们研究了沿着曲折边界中的高空曲面沿孢子品种的爆炸，以爆炸的爆炸来研究。这种品种的镜子是由Gross-Siebert由典型的散射图构建的，该图是使用Abramovich-Chen-Gross-Siebert的刺破日志Gromov-witten不变的。我们表明，在Kontsevich-Soibelman构造的较高维度概括之后，规范散射图和散射图之间存在分段线性同构。我们推断出，可以从这种算法结构中捕获log calabi-yau品种的刺穿的log gromov-witten不变性。作为一个特殊的例子，我们计算了这些不变性，以沿两条线对三维投影空间进行非态度爆破。这将Gross-Pandharipande-Siebert在“热带顶点”上的先前结果推广到更高的维度。
We study log Calabi-Yau varieties obtained as a blow-up of a toric variety along hypersurfaces in its toric boundary. Mirrors to such varieties are constructed by Gross-Siebert from a canonical scattering diagram built by using punctured log Gromov-Witten invariants of Abramovich-Chen-Gross-Siebert. We show that there is a piecewise linear isomorphism between the canonical scattering diagram and a scattering diagram defined algortihmically, following a higher dimensional generalisation of the Kontsevich-Soibelman construction. We deduce that the punctured log Gromov-Witten invariants of the log Calabi-Yau variety can be captured from this algorithmic construction. As a particular example, we compute these invariants for a non-toric blow-up of the three dimensional projective space along two lines. This generalizes previous results of Gross-Pandharipande-Siebert on "The Tropical Vertex" to higher dimensions.
