Cosmic String, Harvey-Moore Conjecture and Family Seiberg-Witten Theory
代数几何
2007-05-23 v1
摘要
In this paper, we study the enumeration of virtual numbers of immersed nodal curves along certain Calabi-Yau K3 fibrations. By using the concept of cosmic strings, we verify the modularity conjeture of the generating function of immersed nodal curves from String theory (Harvey-Moore). Based on the theory defining virtual numbers of nodal curves on algebraic surface (applying to a pencil of lattice polarized K3), a mathematical definition of virtual numbers of immersed rational curves (so-called Gopakumar-Vafa numbers) for Calabi-Yau K3 fibrations is given and it is shown to match up with string theory prediction.
引用
@article{arxiv.math/0409038,
title = {Cosmic String, Harvey-Moore Conjecture and Family Seiberg-Witten Theory},
author = {Ai-Ko Liu},
journal= {arXiv preprint arXiv:math/0409038},
year = {2007}
}
备注
49 pages