论文标题
类型 - $ \ MATHRM {i} $不可记录有限的对称域之间适当的全态图的刚性
Rigidity of proper holomorphic maps between type-$\mathrm{I}$ irreducible bounded symmetric domains
论文作者
论文摘要
我们研究类型 - $ \ mathrm {i} $不可记录的有限对称域之间的适当的全态图。特别是，我们在某些假设下获得了此类地图的刚性结果。更准确地说，让$ f：d^{\ mathrm {i}} _ {p，q} \ to d^{\ mathrm {i}} _ {p'{p'，q'，q'} $是一个合适的全态映射，在$ p \ ge q \ ge q \ ge 2 $和$ q \ ge q \ ge q \ ge q \ ge 2 $和$ q'<然后，我们表明$ p'\ ge p $和$ q'\ ge q $。此外，我们证明存在$ d^$ $ d^{\ mathrm {i}} _ {p，q} $和$ d^{\ mathrm {i}} _ { $ g_h：d^{\ mathrm {i}} _ {p，q} \ to d^{\ mathrm {\ mathrm {i}} _ {p'{p'，q'} $ by \ [g_h（z） \ end {bmatrix} \ quad \ forall \; z \ in d^{\ Mathrm {i}} _ {p，q}，\]其中$ h：d^{\ mathrm {i}} _ {p，q} \ to d^{\ to d^{\ mathrm {\ mathrm {i}}}
We study proper holomorphic maps between type-$\mathrm{I}$ irreducible bounded symmetric domains. In particular, we obtain rigidity results for such maps under certain assumptions. More precisely, let $f:D^{\mathrm{I}}_{p,q}\to D^{\mathrm{I}}_{p',q'}$ be a proper holomorphic map, where $p\ge q\ge 2$ and $q'<\min\{2q-1,p\}$. Then, we show that $p'\ge p$ and $q'\ge q$. Moreover, we prove that there exist automorphisms $ψ$ and $Φ$ of $D^{\mathrm{I}}_{p,q}$ and $D^{\mathrm{I}}_{p',q'}$ respectively, such that $f=Φ\circ G_h\circ ψ$ for some map $G_h:D^{\mathrm{I}}_{p,q}\to D^{\mathrm{I}}_{p',q'}$ defined by \[ G_h(Z):= \begin{bmatrix} Z & {\bf 0}\\ {\bf 0} & h(Z) \end{bmatrix}\quad \forall\; Z\in D^{\mathrm{I}}_{p,q},\] where $h:D^{\mathrm{I}}_{p,q}\to D^{\mathrm{I}}_{p'-p,q'-q}$ is a holomorphic map.
