Noun
/ɪˈlɪptɪk ˈsɜːrfɪs/
An "elliptic surface" is a concept primarily used in the field of algebraic geometry. It is a complex manifold or algebraic variety that is a fiber bundle over a base curve, where the fibers are elliptic curves. Elliptic surfaces are important in the study of complex surfaces, number theory, and mathematical physics. The term is mainly used in written academic contexts and is less common in everyday spoken language.
Frequency of Use: The term appears frequently in mathematical literature and research papers, making it more common in written contexts compared to oral speech.
Translation: Un surface elliptique est définie comme une surface projective lisse équipée d'une fibrilation par des courbes elliptiques.
Researchers are increasingly focusing on the properties of elliptic surfaces in higher-dimensional algebraic geometry.
Translation: Les chercheurs se concentrent de plus en plus sur les propriétés des surfaces elliptiques en géométrie algébrique de dimension supérieure.
The study of elliptic surfaces can lead to significant insights in number theory and cryptography.
The term "elliptic surface" does not typically appear in idiomatic expressions or common phrases, as it is a technical term with a specific meaning in advanced mathematics. However, mathematical language often employs terms that can lead to idiomatic phrases in broader contexts. Here are some expressions related to mathematics that indirectly connect to the concept:
Translation: Avoir seulement une compréhension superficielle d'un sujet sans une profonde compréhension.
On the surface: Appearing one way but possibly different underneath.
Translation: Apparaitre d'une certaine manière mais peut-être différent en dessous.
Drawing a line in the sand: Setting a boundary that signals limits, similar to defining a surface in mathematical terms.
The term "elliptic" comes from the Greek word "elleipsis," meaning "to fall short" or "a failing." This associates with the idea of an ellipse, which is a type of curve. The word “surface” originates from the Latin "superficies," which means "the outer face or appearance."
Synonyms: - Algebraic surface - Elliptic manifold
Antonyms: - Non-elliptic surface - Irregular surface
The term "elliptic surface" captures a significant concept in algebraic geometry, emphasizing the intersection of various mathematical disciplines. Though not commonly used outside academic discussions, it plays an important role in understanding complex structures in mathematics.