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7 papers · 2 filters
Noether's problem and descent
Fedor Bogomolov, Yuri Tschinkel
We study Noether's problem from the perspective of torsors under linear algebraic groups and descent.
Stable rationality of quadric and cubic surface bundle fourfolds
Asher Auel, Christian Böhning, Alena Pirutka
We study the stable rationality problem for quadric and cubic surface bundles over surfaces from the point of view of the degeneration method for the Chow group of 0-cycles. Our ma…
Stable rationality of Brauer-Severi surface bundles
Andrew Kresch, Yuri Tschinkel
For sufficiently ample linear systems on rational surfaces we show that a very general associated Brauer-Severi surface bundle is not stably rational.
Algebraically hyperbolic manifolds have finite automorphism groups
Fedor Bogomolov, Ljudmila Kamenova, Misha Verbitsky
A projective manifold is algebraically hyperbolic if there exists a positive constant such that the degree of any curve of genus on is bounded from above by $A(g-1)…
Classifying surfaces with via group theory
Federico Buonerba, Fedor Bogomolov, Nikon Kurnosov
We give a new proof of a theorem of Bogomolov, that the only surfaces with are those constructed by Hopf and Inoue. The proof follows the strategy of the original…
Specialization of birational types
Maxim Kontsevich, Yuri Tschinkel
We introduce a simplified version of the Grothendieck group of algebraic varieties and use it to show that birational types specialize in families with mild singularities of the ce…