The Geometry of Birationally Commutative Graded Domains.

[摘要] Let R be a graded noetherian domain.If the graded quotient ring of R is of the formK[z, z^{-1}; sigma] for some field Kand automorphism sigma of K, we say that R isbirationally commutative.The main result of this thesis isa complete classification of birationally commutative projective surfaces:birationally commutative domains of Gelfand-Kirillov dimension 3.We show that all such rings are determined by geometric data of a very precise type. This generalizes the work of Rogalski and Staffordon birationally commutative surfaces that are generated in degree 1.A large class of these rings are idealizer subrings of twisted homogeneous coordinate rings.We study these more generally and determine their properties, in particular giving necessary and sufficient conditions for them to be noetherian.We also give a generalized homological version of the Kleiman-Bertini theorem, with applications tothe study of idealizers and of birationally commutative surfaces.

[发布机构] University of Michigan

[效力级别] Noncommutative Algebraic Geometry

[关键词] Birationally Commutative Projective Surface;Noncommutative Algebraic Geometry;Idealizer;Homologically Transverse;Mathematics;Science;Mathematics