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:
“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”
—Simone Weil (1909–1943)