论文标题
圆环圆锥变换的符号结构
The symplectic structure of a toric conic transform
论文作者
论文摘要
假设紧凑型$ r $ $ - 维圆环$ t^r $以圆周形态和汉密尔顿的方式在两极分化的复杂$ d $ d $二维投射歧管上$ m $，而无处可消失的力矩映射$φ$。假设$φ$通过给定的重量$ \boldsymbolν$横向到射线，与这些数据相关联，则有一个复杂的$（d-r+1）$ - 尺寸偏光射击orbifold $ \ hat {m} _ {\boldsymbol务也就是说，$ \ hat {m} _ {\boldsymbolν} $是$ m $两极分化的单位圆圈中射线的反相反图像的合适商。为了澄清这种结构的几何意义，我们考虑了$ m $是复的特殊情况，并表明$ \ hat {m} _ {\boldsymbolν} $本身就是一个kählertoric obifold，它的时刻瞬间是从$ m $ thronform of thronform operative of operative of $ $ $ $ $ $ $ $。
Suppose that a compact $r$-dimensional torus $T^r$ acts in a holomorphic and Hamiltonian manner on polarized complex $d$-dimensional projective manifold $M$, with nowhere vanishing moment map $Φ$. Assuming that $Φ$ is transverse to the ray through a given weight $\boldsymbolν$, associated to these data there is a complex $(d-r+1)$-dimensional polarized projective orbifold $\hat{M}_{\boldsymbolν}$ (referred to as the $\boldsymbolν$-th \textit{conic transform} of $M$). Namely, $\hat{M}_{\boldsymbolν}$ is a suitable quotient of the inverse image of the ray in the unit circle bundle of the polarization of $M$. With the aim to clarify the geometric significance of this construction, we consider the special case where $M$ is toric, and show that $\hat{M}_{\boldsymbolν}$ is itself a Kähler toric obifold, whose moment polytope is obtained from the one of $M$ by a certain "transform", operation (depending on $Φ$ and $\boldsymbolν$).
