A Weil divisor is a locally finite linear combination (with integral coefficients) of irreducible subvarieties of codimension one. The set of Weil divisors forms an abelian group under addition. In the classical theory, where locally finite is automatic, the group of Weil divisors on a variety of dimension n is therefore the free abelian group on the (irreducible) subvarieties of dimension (n − 1). For example, a divisor on an algebraic curve is a formal sum of its closed points. An effective Weil divisor is then one in which all the coefficients of the formal sum are non-negative.
Read more about this topic: Divisor (algebraic Geometry)
Famous quotes containing the word weil:
“If we are suffering illness, poverty, or misfortune, we think we shall be satisfied on the day it ceases. But there too, we know it is false; so soon as one has got used to not suffering one wants something else.”
—Simone Weil (1909–1943)