birational geometry

Noun

 * 1)  A field of algebraic geometry in which the aim is to determine under what conditions two algebraic varieties are isomorphic outside lower-dimensional subsets.
 * 2) * 1999, Yongbin Ruan, Surgery, Quantum Cohomology and Birational Geometry, Ya. Eliashberg, D. Fuchs, T. Ratiu, Alan Weinstein (editors), Northern California Symplectic Geometry Seminar,, Translations, Series 2, Volume 196, page 183,
 * Recently, some amazing relations between quantum cohomology and birational geometry have been discovered.
 * 1) * 2008, Paltin Ionescu, Birational geometry of rationally connected manifolds via quasi-lines, 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 $$\mathbb{P}^n$$ (quasi-lines).
 * 1) * 2009, Claudio Bartocci, Ugo Bruzzo, Daniel Hernández Ruipérez, Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics, Springer (Birkhäuser), Progress in Mathematics 276, page 233,
 * In this chapter we offer some applications of Fourier-Mukai transforms, namely, a classification of the Fourier-Mukai partners of complex projective surfaces, some issues in birational geometry, and an approach to the McKay correspondence via Fourier-Mukai transform.
 * In this chapter we offer some applications of Fourier-Mukai transforms, namely, a classification of the Fourier-Mukai partners of complex projective surfaces, some issues in birational geometry, and an approach to the McKay correspondence via Fourier-Mukai transform.

Translations

 * French: géométrie birationnelle