论文标题
适当的Landau-Ginzburg潜力是开放式镜像图
The proper Landau-Ginzburg potential is the open mirror map
论文作者
论文摘要
配备了反典型的除数$ e $的光滑的光滑的感谢您的Foric Fano表面$ X $是具有超电势的Landau-Ginzburg型号，W。Carl-Pumperla-Siebert使用Pairic demenation of Pairic Demenation of Pairic Demenation of The Traptical Disk的carl-pumperla-siebert，对超电势的定义（x，e）$（x，e）$。当$ e $平滑时，超电势是正确的。我们表明，这种适当的超电球等于在构架零中的规范捆绑包$ k_x $中外部Aganagic-vafa Branes的开放式镜像。结果，适当的Landau-Ginzburg潜力是解决Lerche-Mayr Picard-Fuchs方程的解决方案。 一路上，我们证明了使用量子theta函数的乘法规则，Cadman-Chen对Cadman-Chen的相对Gromov-witten不变性的结果进行了概括。此外，我们概括了HU定理，该定理与从绝对情况到相对情况的爆炸下，将表面的gromov-witten不变性相关联。我们给出的两个证据之一是散射图的异性修改。我们还展示了Hori-Vafa超电势如何通过从复圈室到散射图的无限室的突变与适当的超电势相关。
The mirror dual of a smooth toric Fano surface $X$ equipped with an anticanonical divisor $E$ is a Landau-Ginzburg model with superpotential, W. Carl-Pumperla-Siebert give a definition of the the superpotential in terms of tropical disks using a toric degeneration of the pair $(X,E)$. When $E$ is smooth, the superpotential is proper. We show that this proper superpotential equals the open mirror map for outer Aganagic-Vafa branes in the canonical bundle $K_X$, in framing zero. As a consequence, the proper Landau-Ginzburg potential is a solution to the Lerche-Mayr Picard-Fuchs equation. Along the way, we prove a generalization of a result about relative Gromov-Witten invariants by Cadman-Chen to arbitrary genus using the multiplication rule of quantum theta functions. In addition, we generalize a theorem of Hu that relates Gromov-Witten invariants of a surface under a blow-up from the absolute to the relative case. One of the two proofs that we give introduces birational modifications of a scattering diagram. We also demonstrate how the Hori-Vafa superpotential is related to the proper superpotential by mutations from a toric chamber to the unbounded chamber of the scattering diagram.
