popovvl@mi.ras.ru

Submission: 2015, Apr 19

Exploring Bass' Triangulability Problem on unipotent algebraic subgroups of the affine Cremona groups, we prove a triangulability criterion, the existence of nontriangulable connected solvable affine algebraic subgroups of the Cremona groups, and stable triangulability of such subgroups; in particular, in the stable range we answer Bass' Triangulability Problem is the affirmative. To this end we prove a theorem on invariant subfields of 1-extensions. We also obtain a general construction of all rationally triangulable subgroups of the Cremona groups and, as an application, classify rationally triangulable connected one-dimensional unipotent affine algebraic subgroups of the Cremona groups up to conjugacy.

2010 Mathematics Subject Classification: 20Gxx, 13N15, 14R10

Keywords and Phrases: algebraic variety, the Cremona group, affine algebraic group

Full text: dvi.gz 28 k, dvi 63 k, ps.gz 1095 k, pdf.gz 151 k, pdf 179 k.