How Do You Spell NEF DIVISOR?

Nef divisor, short for nefarious divisor, is a term predominantly used in mathematical literature and specifically in the field of algebraic geometry. A nef divisor refers to a particular type of divisor on a projective algebraic variety or a compact complex manifold. Divisors are essentially mathematical objects that encode the positions of hypersurfaces defined on a variety or manifold. They play a fundamental role in the study of algebraic and differential geometry.

A nef divisor is a divisor D whose intersection with every algebraic curve on the variety or manifold is nonnegative. More precisely, for any algebraic curve C, the intersection number of C with D is greater than or equal to zero. This property ensures that nef divisors have a positive or zero effect when intersecting with algebraic curves.

This positivity condition is a fundamental concept in the study of algebraic and differential geometry, as it allows for the formulation and study of birational geometry and the existence of certain canonical divisors and line bundles. Nef divisors have various applications in the study of numerous geometric questions, such as the characterization of projective varieties, the classification of complex manifolds, and the determination of geometric properties of algebraic varieties.

In conclusion, a nef divisor is a divisor in algebraic geometry that exhibits a nonnegative intersection with every algebraic curve on a variety or manifold, allowing for the analysis of various geometric properties and questions.