Differential Operators on Varieties with a Quotient Subvariety

✍ Scribed by R. Cannings; M.P. Holland

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 747 KB
• Volume: 170
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1994.1363

✦ Synopsis

A finite group ( (;) acts on a smo)th affine variety Spec (A), leaving stable a closed subvariety (\operatorname{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 \backslash \operatorname{Spec} A / J) unchanged is (A^{(i)}+J). For reasonable (G)-actions the ring of differential operators (\rho\left(A^{(i}+J\right)) has a unique minimal non-zero ideal, (J(A)), with the factor isomorphic to ((A / J)^{i}). Particular cases of this construction are considered with emphasis on the problem of when differential operators extend from ((A / J)^{i}) to (A / J . \quad \therefore 11^{6 / 24}) Academic Prem. lnc.