论文标题
通过反射与对称性的曲折表面
Toric surfaces with symmetries by reflections
论文作者
论文摘要
让$ w $是飞机上的反射组，在$ w $ action下不变的有理多边形$ p $。 $ w $在$ p $上的动作引起了与$ p $相关的感谢您的福利$ x_p $的$ w $。在本文中，我们研究了$ w $ - 代表$ h^\ ast（x_p）$，并证明不变的子$ h^\ ast（x_p）^w $与\ emph {pentamental actail {undemental actamental actamental actamental actamental actamental actamental actamental actamental actamental aincemology ring是同构的。例如，我们提供了与$ g_2 $类型的Weyl Chambers相关的曲折品种情况的主要结果的明确描述。
Let $W$ be a reflection group in a plane and $P$ a rational polygon that is invariant under the $W$-action. The action of $W$ on $P$ induces a $W$-action on the toric variety $X_P$ associated with $P$. In this paper, we study the $W$-representation on the cohomology $H^\ast(X_P)$ and show that the invariant subring $H^\ast(X_P)^W$ is isomorphic to the cohomology ring of the toric variety associated with the \emph{fundamental region}~$P/W$. As an example, we provide an explicit description of the main result for the case of the toric variety associated with the fan of Weyl chambers of type $G_2$.
