ruled surfaces的规范理论等变Gromov-Witten不变量和完全Seiberg-Witten不变量
Gauge theoretical equivariant Gromov-Witten invariants and the full Seiberg-Witten invariants of ruled surfaces
摘要：
设$(F,J,ω)$是几乎Kähler流形，$α$是紧李群$\hat K$在$F$上的$J$ -全纯作用，$K$是$\hat K$的闭正规子群，它使$ω$不变.我们介绍了这种三元组$(F,α,K)$的规范理论不变量。这些不变量与黎曼曲面上某个涡型方程解的模空间有关。给出了三元组$(\Hom(\C^r,\C^{r_0}), α_{\rm can},U(r))$的模空间的显式描述，其中$α_{\rm can}$表示$\hat K=U(r)\times U(r_0)$在$\Hom(\C^r,\C^{r_0})$上的正则作用.在交换情形下，$r=1$的新不变量可以显式计算，并与直纹曲面的完全Seiberg-Witten不变量相一致。
英文摘要：
Let $(F,J,ω)$ be an almost Kähler manifold, $α$ a $J$-holomorphic action of a compact Lie group $\hat K$ on $F$, and $K$ a closed normal subgroup of $\hat K$ which leaves $ω$ invariant. We introduce gauge theoretical invariants for such triples $(F,α,K)$. The invariants are associated with moduli spaces of solutions of a certain vortex type equation on a Riemann surface. We give explicite descriptions of the moduli spaces associated with the triple $(\Hom(\C^r,\C^{r_0}), α_{\rm can},U(r))$, where $α_{\rm can}$ denotes the canonical action of $\hat K=U(r)\times U(r_0)$ on $\Hom(\C^r,\C^{r_0})$. In the abelian case $r=1$, the new invariants can be computed expliciteley and identified with the full Seiberg-Witten invariants of ruled surfaces.
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