The rationality problem for conic bundles

Abstract

This expository paper is concerned with the rationality problems for three-dimensional algebraic varieties with a conic bundle structure. We discuss the main methods of this theory. We sketch the proofs of certain principal results, and present some recent achievements. Many open problems are also stated.

87 pages, LaTeX, expository paper submitted to Uspeshi Mat. Nauk

References in corpus (2)

• Threefold extremal contractions of type IA
• On the unirationality of 3-fold conic bundles

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• Finite groups of bimeromorphic selfmaps of non-uniruled Kähler threefolds
• Sarkisov Links with centres space curves on smooth cubic surfaces
• On the birational geometry of sextic threefold hypersurface in $\mathbf{P}(1,1,2,2,3)$
• Icosahedron in birational geometry
• Conic bundle structures on Q-Fano threefolds
• On 3-folds having a holomorphic torus action with 6 fixed points