Anagram & Information om | Engelska ordet BIRATIONAL

Exempel på hur man kan använda BIRATIONAL i en mening

• These results often feed back into complex algebraic geometry, and for example recently the classification of Fano manifolds using K-stability has benefited tremendously both from techniques in analysis and in pure birational geometry.
• Typically, this happens because a birational morphism contracts some subvarieties of X to points in Y.
• In general a (non-singular) curve of genus 0 is rationally equivalent over K to a conic C, which is itself birationally equivalent to projective line if and only if C has a point defined over K; geometrically such a point P can be used as origin to make explicit the birational equivalence.
• For example, when X is also rationally connected over the complex numbers, the Brauer group of X is isomorphic to the torsion subgroup of the singular cohomology group , which is therefore a birational invariant.
• This states that any birational map between algebraic surfaces is given by a finite sequence of blowups and blowdowns.
• An important tool of modern birational geometry is inversion of adjunction, which allows one to deduce results about the singularities of X from the singularities of D.
• Blowups are the most fundamental transformation in birational geometry, because every birational morphism between projective varieties is a blowup.
• students in different problems of birational geometry, including Fields medallist Caucher Birkar, Florin Ambro, Ivan Cheltsov, Jihun Park, Sung Rak Choi, Yifei Chen, Joseph Cutrone, and Nicholas Marshburn.
• Abrosimov proved that holomorphic automorphisms of a quadric of codimension two are furnished by birational transformations of degree two.
• In the Fano case these intersection numbers, which involve the anticanonical divisor of the variety and its test configuration, can be given powerful alternative characterisations in terms of the algebraic and birational geometry of the Fano variety.

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