Divisor groups¶
AUTHORS:
- David Kohel (2006): Initial version
- Volker Braun (2010-07-16): Documentation, doctests, coercion fixes, bugfixes.
-
sage.schemes.generic.divisor_group.
DivisorGroup
(scheme, base_ring=None)¶ Return the group of divisors on the scheme.
INPUT:
scheme
– a scheme.base_ring
– usually either \(\ZZ\) (default) or \(\QQ\). The coefficient ring of the divisors. Not to be confused with the base ring of the scheme!
OUTPUT:
An instance of
DivisorGroup_generic
.EXAMPLES:
sage: from sage.schemes.generic.divisor_group import DivisorGroup sage: DivisorGroup(Spec(ZZ)) Group of ZZ-Divisors on Spectrum of Integer Ring sage: DivisorGroup(Spec(ZZ), base_ring=QQ) Group of QQ-Divisors on Spectrum of Integer Ring
-
sage.schemes.generic.divisor_group.
DivisorGroup_curve
¶ Special case of the group of divisors on a curve.
-
sage.schemes.generic.divisor_group.
DivisorGroup_generic
¶ The divisor group on a variety.
-
sage.schemes.generic.divisor_group.
is_DivisorGroup
(x)¶ Return whether
x
is aDivisorGroup_generic
.INPUT:
x
– anything.
OUTPUT:
True
orFalse
.EXAMPLES:
sage: from sage.schemes.generic.divisor_group import is_DivisorGroup, DivisorGroup sage: Div = DivisorGroup(Spec(ZZ), base_ring=QQ) sage: is_DivisorGroup(Div) True sage: is_DivisorGroup('not a divisor') False