Regular actions of semi simple algebraic groups on projective threefolds, especially SL(2). (English) Zbl 0704.14038

Nakano, Tetsuo

Group actions and invariant theory, Proc. Conf., Montreal/Can. 1988, CMS Conf. Proc. 10, 137-155 (1989).

[For the entire collection see Zbl 0679.00007.]
This note is a survey on the smooth complex projective threefolds on which SL(2) acts regularly with a nonempty open orbit (i.e. the “quasi- homogeneous threefolds of SL(2)”) and it contains ample references on this subject. - In particular, the analysis of the contraction maps of the extremal rays, according to the Mori theory, and some classical results on the finite subgroups of SL(2) give a complete classification and an explicit description of the relatively minimal models of the quasi-homogeneous threefolds of SL(2).

Reviewer: L.Picco Botta

MSC:

14L30	Group actions on varieties or schemes (quotients)
14J30	\(3\)-folds
14C20	Divisors, linear systems, invertible sheaves
14E30	Minimal model program (Mori theory, extremal rays)
14M17	Homogeneous spaces and generalizations

Keywords:

quasi-homogeneous threefolds of SL(2); extremal rays; Mori theory; minimal models

Citations:

Zbl 0679.00007