HYPERPLANE DIVISOR Meaning and
Definition
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A hyperplane divisor is a fundamental concept in algebraic geometry and refers to a specific type of algebraic variety. To understand this term, it is essential to first comprehend the individual components: hyperplanes and divisors.
A hyperplane, in mathematics, is a subspace of one dimension less than the ambient space it is situated in, dividing it into two parts. In geometric terms, a hyperplane in three-dimensional space is a two-dimensional plane, while in n-dimensional space, it has n-1 dimensions.
A divisor, on the other hand, is a mathematical object that describes the number of zeros and poles of a given function or equation. In algebraic geometry, it represents a divisor of a function that consists of the set of points where the function vanishes or has a pole.
Combining these two concepts, a hyperplane divisor represents a special type of divisor that corresponds to the zeros or poles of a hyperplane equation. More precisely, in algebraic geometry, a hyperplane divisor is a hypersurface defined by a linear equation in n-dimensional projective space. It divides the ambient space into two parts and is characterized by the set of points where the equation holds true.
Overall, a hyperplane divisor is a geometric object or variety that represents the zeros or poles of a linear equation in algebraic geometry. It plays a significant role in various mathematical applications, such as intersection theory, algebraic curves, and algebraic surfaces.
Etymology of HYPERPLANE DIVISOR
The term "hyperplane" originated from the combination of two Greek words: "hyper", meaning "over" or "beyond", and "plane", which refers to a flat, two-dimensional surface. It is considered a generalization of the term "plane" to higher dimensions.
The word "divisor" comes from the Latin term "dividere", meaning "to divide". In mathematics, a divisor is a number or expression that divides another number or expression evenly without a remainder. However, in the context of "hyperplane divisor", the term translates into a different concept.
The etymology of the complete term "hyperplane divisor" lies in algebraic geometry, a field that explores the connection between algebra and geometry. In this context, a "hyperplane" is a flat subspace or a multidimensional surface that splits the given space into two regions.
