Invariant tensor fields and orbit varieties for finite algebraic transformation groups
| dc.creator | Losik, Mark | |
| dc.creator | Michor, Peter W. | |
| dc.creator | Popov, Vladimir L. | |
| dc.date | 2002-06-03 | |
| dc.date | 2002-09-02 | |
| dc.date.accessioned | 2026-07-07T06:26:26Z | |
| dc.date.available | 2026-07-07T06:26:26Z | |
| dc.description | Let $X$ be a smooth algebraic variety endowed with an action of a finite group $G$ such that there exists the geometric quotient $π_X:X\to X/G$. We characterize rational tensor fields $τ$ on $X/G$ such that the {\it pull back} of $τ$ is regular on $X$: these are precisely all $τ$ such that $\operatorname{div}_{R_{X/G}}(τ)\ge 0$ where $R_{X/G}$ is the {\it reflection divisor} of $X/G$ and $\operatorname{div}_{R_{X/G}}(τ)$ is the {\it $R_{X/G}$-divisor} of $τ$. We give some applications, in particular to the generalization of Solomon's theorem. In the last section we show that if $V$ is a finite dimensional vector space and $G$ a finite subgroup of $\operatorname{GL}(V)$, then each automorphism $ψ$ of $V/G$ admits a biregular lift $ϕ: V\to V$ provided that $ψ$ maps the regular stratum to itself and $ψ_*(R_{X/G})=R_{X/G}$. | |
| dc.description | AmSTeX, revised version with 27 pages. More detailed proofs, small mistakes corrected | |
| dc.identifier | https://arxiv.org/abs/math/0206008 | |
| dc.identifier | http://arxiv.org/abs/math/0206008 | |
| dc.identifier | In: A Tribute to C.S.Seshadri: Perspectives in Geometry and Representation Theory. Hindustan Book Agency, also Trends Math., Birkhäuser, Basel, 2003, 346--378 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/97105 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Representation Theory | |
| dc.subject | 14L24; 14L30 | |
| dc.title | Invariant tensor fields and orbit varieties for finite algebraic transformation groups | |
| dc.type | text |