论文标题
分支的投影结构，分支SO（3，C） - 驾驶器和对数连接
Branched projective structures, branched SO(3,C)-opers and logarithmic connections on jet bundle
论文作者
论文摘要
我们在紧凑的Riemann Surface $ x $上研究带有固定分支的除数$ s \，= \，\ sum_ {i = 1}^d x_i $，其中$ x_i \，\ in \ in x $的分支。在定义了分支的$ {\ rm so}（3，{\ Mathbb c}）$ - OPERS之后，我们表明，$ x $上的分支霍明型投射结构是天然的，带有分支$ {\ rm so}（\ rm so}}（3，3，{\ mathbb c}）$ - opers $ - opers $ - opers $ s $ s $ s $ s $ s $ s $。可以确定的是，$ x $上的分支全体形态投影结构也被确定为$ j^2（（（tx）\ otimes {\ Mathcal o} _x _x（s）$ s singular singular y $ s $，满足某些自然的自然重要性条件，$ j^2（（tx）\ otimes {\ mathcal o} _x _x（s）$。
We study the branched holomorphic projective structures on a compact Riemann surface $X$ with a fixed branching divisor $S\, =\, \sum_{i=1}^d x_i$, where $x_i \,\in\, X$ are distinct points. After defining branched ${\rm SO}(3,{\mathbb C})$--opers, we show that the branched holomorphic projective structures on $X$ are in a natural bijection with the branched ${\rm SO}(3,{\mathbb C})$--opers singular at $S$. It is deduced that the branched holomorphic projective structures on $X$ are also identified with a subset of the space of all logarithmic connections on $J^2((TX)\otimes {\mathcal O}_X(S))$ singular over $S$, satisfying certain natural geometric conditions.
