Noun Phrase
/ˈloʊ.kəl.i æˈnæl.ɪ.tɪk ˈvær.ɪ.ti/
A "locally analytic variety" is a concept from algebraic geometry and complex analysis, referring to a particular type of mathematical structure that satisfies certain conditions analogous to the behavior of analytic functions in a local neighborhood. In simpler terms, it recognizes a variety (a solution set of polynomial equations) that behaves well under analytic continuation.
The phrase is used primarily in written contexts such as academic papers, textbooks, and advanced mathematics discussions. It is not commonly used in everyday speech.
"The locally analytic variety plays a crucial role in understanding the properties of algebraic spaces."
"La variedad analítica local juega un papel crucial en la comprensión de las propiedades de los espacios algebraicos."
"Researchers are exploring how locally analytic varieties can be utilized in the study of complex manifolds."
"Los investigadores están explorando cómo las variedades analíticas locales pueden ser utilizadas en el estudio de variedades complejas."
"Understanding the structure of a locally analytic variety helps in solving complex differential equations."
"Comprender la estructura de una variedad analítica local ayuda a resolver ecuaciones diferenciales complejas."
The term "locally analytic variety" isn't common in idiomatic expressions as it is highly specialized terminology within mathematics. However, related ideas in mathematics may lead to certain expressions; here are a few examples using broader mathematical language:
"In the realm of locally analytic varieties, one must consider the limits of their behavior."
"En el ámbito de las variedades analíticas locales, se deben considerar los límites de su comportamiento."
"When we examine the roots of locally analytic varieties, we often uncover deeper insights about their structure."
"Cuando examinamos las raíces de las variedades analíticas locales, a menudo descubrimos perspectivas más profundas sobre su estructura."
"Many theorems in algebraic geometry rely on properties derived from locally analytic varieties."
"Muchos teoremas en geometría algebraica se basan en propiedades derivadas de las variedades analíticas locales."
The term "locally analytic variety" is derived from: - "Local" comes from Latin "localis," meaning pertaining to a place. - "Analytic" originates from the Greek "analytikos," meaning able to be unloosed or solved, which relates to the analysis of functions. - "Variety" comes from Latin "varietas," meaning diversity and referring to a collection of solutions that meet certain polynomial criteria.
Synonyms: - Analytic space - Algebraic variety (in broader terms)
Antonyms: - Non-analytic variety - Discrete set
This comprehensive overview of "locally analytic variety" offers insight into both its mathematical significance and its linguistic context.