论文标题
在Kähler指标的空间中，带有$ t $ -Smorgemery的地球射线
Geodesic rays in the space of Kähler metrics with $T$-symmetry
论文作者
论文摘要
令$（m，ω，j）$为kähler歧管，配备有效的汉密尔顿圆环动作$ρ：t \ rightarrow \ mathrm {diff}（m，m，ω，j）$ by Isometries，MOMM MAM MAP $μ：m \ rightArrow \ rightarrow \ rightarrow \ rightarrow \ mathfrak \ mathfrak {我们首先在$ m $上构造了一个单数混合极化$ \ mathcal {p} _ {\ Mathrm {mathrm {mix}} $。其次，我们在$ m $上构建了一个与$ω$兼容的复杂结构的单参数家族$ j_ {t} $。此外，当$ m $紧凑时，相应的kähler指标$ g_ {t} $的路径是$ m $ $ m $的完整地理射线。最后，我们证明了Kähler极化的相应家族$ \ MATHCAL {p} _ {t} $与$ j_ {t} $关联到$ \ Mathcal {p} _ {\ Mathrm {mathrm {mix}} $ as $ t \ rightarrow \ rightarrow \ infty \ infty \ infty $ \ rightcal {p}
Let $(M, ω, J)$ be a Kähler manifold, equipped with an effective Hamiltonian torus action $ρ: T \rightarrow \mathrm{Diff}(M, ω, J)$ by isometries with moment map $μ: M \rightarrow \mathfrak{t}^{*}$. We first construct a singular mixed polarization $\mathcal{P}_{\mathrm{mix}}$ on $M$. Second, we construct a one-parameter family of complex structures $J_{t}$ on $M$ which are compatible with $ω$. Furthermore, the path of corresponding Kähler metrics $g_{t}$ is a complete geodesic ray in the space of Kähler metrics of $M$, when $M$ is compact. Finally, we show that the corresponding family of Kähler polarizations $\mathcal{P}_{t}$ associated to $J_{t}$ converges to $\mathcal{P}_{\mathrm{mix}}$ as $t \rightarrow \infty$.
