Convergence of Hermitian-Yang-Mills Connections on Kähler Surfaces and mirror symmetry
| dc.creator | Nishinou, Takeo | |
| dc.date | 2003-01-28 | |
| dc.date | 2004-10-30 | |
| dc.date.accessioned | 2026-07-07T04:54:44Z | |
| dc.date.available | 2026-07-07T04:54:44Z | |
| dc.description | The purpose of this paper is to exhibit a natural construction between complex geometry and symplectic geometry following the idea of mirror symmetry. Suppose we are given a family of pairs of 2-dimensional Kähler tori and stable holomorphic vector bundles on them $(\hat M_{\ep}, E_{\ep})$, \ep \in (0, 1]$, and each has structure of a Lagrangian torus fibration $π:\hat M_{\ep} \to B$ whose fibers are of diameter $O(\ep)$, and let $A_{\ep}$ be a family of hermitian Yang-Mills(HYM) connections on $E_{\ep}$. As $\ep$ goes to zero, $A_{\ep}$ will, modulo possible bubbles, converge to a connection which is flat on each fiber. Since each fiber is a torus, limit connection will determine elements of the dual torus, which are points of the fiber of the mirror $M_1$. These points gather to make up (special) Lagrangian variety. | |
| dc.description | Title changed. Extensive revision | |
| dc.identifier | https://arxiv.org/abs/math/0301324 | |
| dc.identifier | http://arxiv.org/abs/math/0301324 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66370 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.title | Convergence of Hermitian-Yang-Mills Connections on Kähler Surfaces and mirror symmetry | |
| dc.type | text |