Definition of Birational. Meaning of Birational. Synonyms of Birational

- In mathematics, birational geometry is a field of algebraic geometry in which the goal is to determine when two algebraic varieties are isomorphic outside...
- prin****lly as the first to give a classification of algebraic surfaces in birational geometry, and other contributions in algebraic geometry. Enriques was...
- Harvard in 1960, Hironaka received his PhD for his thesis On the Theory of Birational Blowing-up. Hironaka was an ****ociate Professor of Mathematics at Brandeis...
- geometric genus p g {\displaystyle p_{g}} because one cannot distinguish birationally only the topological genus. Then, irregularity is introduced for the...
- In algebraic geometry, a birational invariant is a property that is preserved under birational equivalence. A birational invariant is a quantity or object...
- contracted. Then, the birational map is given by normalization. Two varieties are said to be birationally equivalent if there exists a birational map between them;...
- proved by Oscar Zariski (1943), is a statement about the structure of birational morphisms stating roughly that there is only one branch at any normal...
- canonical ring and therefore likewise the Kodaira dimension is a birational invariant: Any birational map between smooth compact complex manifolds induces an isomorphism...
- surfaces and Mori fiber spaces. The following perspective is crucial in birational geometry (in particular in Mori's minimal model program). Let X {\displaystyle...
- Equivalently, they are birationally equivalent if their function fields are isomorphic. An affine variety is a rational variety if it is birationally equivalent to...