论文标题
Kahler极化对复杂品种混合极化的变性
Degeneration of Kahler polarizations to mixed polarizations on toric varieties
论文作者
论文摘要
令$（x，ω，j）$为delzant polytope确定的尺寸$ 2N $的复曲。在本文中，我们首先构建了hamiltonian $ t^{k} $的偏光$ \ shp_ {k} $ - $ x $上的操作（请参阅Theorem 3.11）。我们将证明$ \ shp_ {k} $是$ 1 \ le k <n $的单一混合两极化，而$ \ shp_ {n} $是一个单一的真实极化，与\ cite {bfmn}中研究的真实极化相吻合。然后，对于每个$ 1 \ le K \ le n $，我们将在$ x $上找到一个单参数家族$ \ shp_ {k，t} $，它收敛到$ \ shp_ {k {k {k} $（请参阅Theorem 3.12）。最后，我们将证明$ \ shh_ {k，t}^{t} $ $ t^{k} $的空间 - 不变$ j_ {k，t} $ - holomorphic部分收集到$ \ shh_ {k shh_ {k}^{0} $（请参阅theorem 3.18）。
Let $(X, ω, J)$ be a toric variety of dimension $2n$ determined by a Delzant polytope. In this paper, we first construct the polarizations $\shP_{k}$ by the Hamiltonian $T^{k}$-action on $X$ (see Theorem 3.11). We will show that $\shP_{k}$ is a singular mixed polarization for $1\le k < n$, and $\shP_{n}$ is a singular real polarization which coincides with the real polarization studied in \cite{BFMN} on the open dense subset of $X$. Then for each $1\le k \le n$, we will find a one-parameter family of Kähler polarizations $\shP_{k,t}$ on $X$ that converges to $\shP_{k}$ (see Theorem 3.12). Finally, we will show that $\shH_{k,t}^{T}$ the space of $T^{k}$-invariant $J_{k,t}$-holomorphic sections converges to $\shH_{k}^{0}$ (see Theorem 3.18).
