Differential Operators on Varieties with a Quotient Subvariety
Differential Operators on Varieties with a Quotient Subvariety
复制标题
具有商子品种的品种上的微分算子
DOI：
10.1006/jabr.1994.1363
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发表时间：
1994
影响因子：
0.9
通讯作者：
M. P. Holland
中科院分区：
文献类型：
--
作者：
R. C. Cannings;M. P. Holland
有限群G作用在光滑仿射簇SpecA上，留下稳定的闭子簇SpecA/ J。从Spec A通过用它的商（Spec A / J）/ G替换Spec A / J并保持补数Spec A \Spec A / J不变而得到的簇上的函数环是AG + J。对于合理的G -作用，微分算子环D（AG + J）有唯一的极小非零理想JD（A），其因子同构于D（A / J）G。特殊情况下，这种建设被认为是重点的问题时，微分算子从（A / J）G到A / J。
Abstract A finite group G acts on a smooth affine variety Spec A , leaving stable a closed subvariety Spec A / J . The ring of functions on the variety obtained from Spec A by replacing Spec A / J by its quotient (Spec A / J )/ G and leaving the complement Spec A \Spec A / J unchanged is A G + J . For reasonable G -actions the ring of differential operators D ( A G + J ) has a unique minimal non-zero ideal, J D ( A ), with the factor isomorphic to D ( A / J ) G . Particular cases of this construction are considered with emphasis on the problem of when differential operators extend from ( A / J ) G to A / J .