birational geometry

[baɪˈreɪʃənəl dʒiˈɒmətri]
noun
geometria biracional
1. A branch of algebraic geometry that studies properties of algebraic varieties that are invariant under birational maps, which are rational maps with rational inverses
Birational geometry allows mathematicians to classify algebraic varieties by identifying those that are equivalent under birational transformations.
A geometria biracional permite que matemáticos classifiquem variedades algébricas identificando aquelas que são equivalentes sob transformações biracionais.
2. The study of geometric structures that remain unchanged under birational equivalence, focusing on properties like dimension and singularities
In birational geometry, two varieties are considered equivalent if there exists a birational map between them.
Em geometria biracional, duas variedades são consideradas equivalentes se existe um mapa biracional entre elas.
This is a specialized technical term used primarily in academic mathematics. It appears in university-level algebraic geometry courses and research publications in both Brazil and Portugal. The term maintains the same meaning and usage across all Portuguese-speaking regions, with no significant regional variations. It is part of the standard mathematical lexicon taught in graduate programs at major institutions like USP (Universidade de São Paulo) and IMPA (Instituto Nacional de Matemática Pura e Aplicada) in Brazil.
Synonyms / Sinônimos
birational algebraic geometryrational geometry

Regional Variations

General Brazilian
geometria biracional
Standard academic term used in Brazilian universities and mathematical publications
Portugal
geometria biracional
Same term used in Portuguese academic mathematics; sometimes found in older texts as 'geometria de transformações biracionais'
International Academic
geometria biracional
Standardized term across all Portuguese-speaking mathematical communities

Related Words

algebraic geometrybirational mapvarietysingularitiesrational mapblow-upresolution of singularities
Look up more words on Fala2Me
The free English-Portuguese dictionary with real Brazilian accents, NYC slang, conjugator and more
Open Fala2Me →