On embeddings of certain spherical homogeneous spaces in prime characteristic
On embeddings of certain spherical homogeneous spaces in prime characteristic
复制标题
关于素数特征中某些球形齐次空间的嵌入
DOI：
--
复制
发表时间：
2011
期刊：
影响因子：
--
通讯作者：
R. Tange
中科院分区：
文献类型：
--
作者：
R. Tange
设$Mathcal{G}$是特征为p >； 0的代数闭域上的约化群.我们研究了由G- × G-空间G诱导的齐次$数学{G}-空间的嵌入，G是一个合适的约化群，沿着$数学{G}$的抛物子群嵌入.我们给出了标准因子和B-半不变函数的标准因子的显式公式。此外，我们还证明了，在某些温和的假设下，这种齐次空间的任何(正规)等变嵌入都是典型的Frobenius分裂相容于某些子簇的，并且具有环面嵌入的等变有理分解。特别是，所有这些嵌入都是Cohen-Macaulay的。例如，单位群为G的正规可约么半群中的G- × G-轨道。另一个例子是著名的行列式变元和(圆形)复形变元的开式{G}-轨道。最后，我们研究了各种圆形复形的Gorenstein性质和一个相关的还原么半群。
Let $ mathcal{G} $ be a reductive group over an algebraically closed field of characteristic p > 0. We study embeddings of homogeneous $ mathcal{G} $-spaces that are induced from the G × G-space G, G a suitable reductive group, along a parabolic subgroup of $ mathcal{G} $. We give explicit formulas for the canonical divisors and for the divisors of B-semi-invariant functions. Furthermore, we show that, under certain mild assumptions, any (normal) equivariant embedding of such a homogeneous space is canonically Frobenius split compatible with certain subvarieties and has an equivariant rational resolution by a toroidal embedding. In particular, all these embeddings are Cohen–Macaulay. Examples are the G × G-orbits in normal reductive monoids with unit group G. Further examples are the open $ mathcal{G} $-orbits of the well known determinantal varieties and the varieties of (circular) complexes. Finally, we study the Gorenstein property for the varieties of circular complexes and for a related reductive monoid.