臺灣大學: 數學研究所林惠雯賴冠文Lai, Kuan-WenKuan-WenLai2013-03-212018-06-282013-03-212018-06-282011http://ntur.lib.ntu.edu.tw//handle/246246/249934在這篇文章中，我概述了關於Gromov-Witten不變量與Hurwitz數之間如何建立對應的工作，以及詳細探討Toda階序的Hirota方程。該階序能夠提供相當程度的遞迴關係以計算射影直線上的Gromov-Witten不變量。主要的參考文獻為A. Okounkov與R. Pandharipande的一系列論文[11, 12]。In this article, I would like to outline the work about the correspondence between Gromov-Witten invariants and Hurwitz numbers, and concentrate mainly on the detailed study of Hirota equations for the Toda hierarchy which provides certain recurrence relations for relative Gromov-Witten invariants of P1. The papers of A. Okounkov and R. Pandharipande [11, 12] are the main sources of my study.519815 bytesapplication/pdfen-USELSV方程Gromov-Witten理論Hurwitz數τ-函數Toda階序完備輪換偏移對稱函數無限維楔表示論completed cycleELSV formulaGromov-Witten theoryHurwitz numberinfinite wedge representationshifted symmetric functionτ-functionToda hierarchythesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/249934/1/ntu-100-R98221026-1.pdf