Birational geometry

English

Noun

1. Template:Lb A field of algebraic geometry in which the aim is to determine under what conditions two algebraic varieties are isomorphic outside lower-dimensional subsets.

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   • 1999, Yongbin Ruan, Surgery, Quantum Cohomology and Birational Geometry, Ya. Eliashberg, D. Fuchs, T. Ratiu, Alan Weinstein (editors), Northern California Symplectic Geometry Seminar, Template:W, 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 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).

   • 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.

Related terms

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Translations

• French: Template:T

See also

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Further reading

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• Birational geometry on Template:W