Weil divisors on schemes
A prime divisor on is a closed integral subscheme of codimension one. We define an abelian group generated by the prime divisors on . A Weil divisor is an element of . Thus, a Weil divisor can be written as:
where the sum is over all the prime divisors of , the are integers and only finitely many of them are non-zero. A degree of a divisor is defined to be . Finally, a divisor is said to be effective if for all the prime divisors .
For more information, see Hartshorne’s book listed in the bibliography for algebraic geometry.
|Title||Weil divisors on schemes|
|Date of creation||2013-03-22 15:34:08|
|Last modified on||2013-03-22 15:34:08|
|Last modified by||alozano (2414)|
|Defines||regular in codimension one|