论文标题
明确的Abelian Instantons on $ s^1 $ -invariantKählerEinstein $ 6 $ -Manifolds
Explicit abelian instantons on $S^1$-invariant Kähler Einstein $6$-manifolds
论文作者
论文摘要
我们考虑降低（变形的）Hermitian Yang-Mills条件（$ S^1 $ -InvariantKählerEinstein $ 6 $ -Manifolds）。这使我们可以根据商的数据来重新重新重新制定（变形的）Hermitian Yang-Mills方程，Kähler$ 4 $ -Manifold。特别是，我们将此构造应用于$ \ Mathbb {C} \ Mathbb {P}^2 $的规范捆绑包，该构造与Calabi Ansatz Metric赋予了明显的Abelian $ su（3）$ instantons，我们表明这些频谱由$ \ m m i \ mathbb {c} c} \ mathbbbbbbbbbbbbbbb {p} $} 2 $} p^2 $ {p。我们还发现了$ 1 $ - 参数的明显变形的Hermitian Yang-Mills连接。作为我们调查的副产品，我们找到了其全态体积形式的坐标表达式，该表达式导致我们构建了$ \ Mathcal {o} _ {\ Mathbb {c} \ Mathbb {c} \ Mathbb {p}^2}^2}（-3）$的特殊拉格朗日叶子。
We consider a dimensional reduction of the (deformed) Hermitian Yang-Mills condition on $S^1$-invariant Kähler Einstein $6$-manifolds. This allows us to reformulate the (deformed) Hermitian Yang-Mills equations in terms of data on the quotient Kähler $4$-manifold. In particular, we apply this construction to the canonical bundle of $\mathbb{C}\mathbb{P}^2$ endowed with the Calabi ansatz metric to find explicit abelian $SU(3)$ instantons and we show that these are determined by the spectrum of $\mathbb{C}\mathbb{P}^2$. We also find $1$-parameter families of explicit deformed Hermitian Yang-Mills connections. As a by-product of our investigation we find a coordinate expression for its holomorphic volume form which leads us to construct a special Lagrangian foliation of $\mathcal{O}_{\mathbb{C}\mathbb{P}^2}(-3)$.
