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Divisor (algebraic geometry)

In algebraic geometry, divisors are a generalization of codimension-1 subvarieties of algebraic varieties. Two different generalizations are in common use, Cartier divisors and Weil divisors (named for Pierre Cartier and André Weil by David Mumford). Both are derived from the notion of divisibility in the integers and algebraic number fields.

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Divisors on a Riemann surface

Weil divisors

Divisor class group

Cartier divisors

Functoriality

The first Chern class

Global sections of line bundles and linear systems

The Grothendieck–Lefschetz hyperplane theorem

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Divisor (algebraic geometry)

Nodes116
Edges115
Triples0
Avg. degree1.98
Density0.017241
Components1

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divisor displaystyle cartier divisors mathcal weil defined projective group field class line degree one variety scheme effective dimension principal sheaf

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