birational geometry
English edit
Noun edit
birational geometry (uncountable)
 (algebraic geometry) A field of algebraic geometry in which the aim is to determine under what conditions two algebraic varieties are isomorphic outside lowerdimensional subsets.
 Birational geometry amounts to the study of mappings given by rational functions rather than polynomials.
 1999, Yongbin Ruan, Surgery, Quantum Cohomology and Birational Geometry, Ya. Eliashberg, D. Fuchs, T. Ratiu, Alan Weinstein (editors), Northern California Symplectic Geometry Seminar, American Mathematical Society, Translations, Series 2, Volume 196, page 183,
 Recently, some amazing relations between quantum cohomology and birational geometry have been discovered.
 2008, Paltin Ionescu, Birational geometry of rationally connected manifolds via quasilines, Ciro Ciliberto, et al., Projective Varieties with Unexpected Properties, Walter de Gruyter, page 317,
 This is, mostly, a survey of results about the birational geometry of rationally connected manifolds, using rational curves analogous to lines in (quasilines).
 2009, Claudio Bartocci, Ugo Bruzzo, Daniel Hernández Ruipérez, FourierMukai and Nahm Transforms in Geometry and Mathematical Physics, Springer (Birkhäuser), Progress in Mathematics 276, page 233,
 In this chapter we offer some applications of FourierMukai transforms, namely, a classification of the FourierMukai partners of complex projective surfaces, some issues in birational geometry, and an approach to the McKay correspondence via FourierMukai transform.
Related terms edit
 birational automorphism
 birational automorphism group
 birational equivalence
 birational invariant
 birational mapping
 birational morphism
Translations edit
field of algebraic geometry

See also edit
Further reading edit
 Abundance conjecture on Wikipedia.Wikipedia
 Blowing up on Wikipedia.Wikipedia
 Birational geometry on Encyclopedia of Mathematics