Divisor (algebraic geometry): Difference between revisions
Jump to navigation
Jump to search
imported>Chris Day No edit summary |
mNo edit summary |
||
Line 15: | Line 15: | ||
The ''support'' of a divisor is the set of points with non-zero coefficients in the sum. | The ''support'' of a divisor is the set of points with non-zero coefficients in the sum. | ||
The divisor of a function ''f'', denoted <math>(f)</math> or <math>\mathop{\mathrm{div}} f</math>, is supported on the [[pole]]s and [[zero]]es of the function, with coefficients the degree of the pole or zero, with positive sign for zeroes and negative sign for poles. The degree of the divisor of a function is zero. | The divisor of a function ''f'', denoted <math>(f)</math> or <math>\mathop{\mathrm{div}} f</math>, is supported on the [[pole]]s and [[zero]]es of the function, with coefficients the degree of the pole or zero, with positive sign for zeroes and negative sign for poles. The degree of the divisor of a function is zero.[[Category:Suggestion Bot Tag]] |
Latest revision as of 07:00, 8 August 2024
![](http://s9.addthis.com/button1-share.gif)
In geometry a divisor on an algebraic variety is a formal sum (with integer coefficients) of subvarieties.
An effective divisor is a sum with non-negative integer coefficients.
Divisors on a curve
On an algebraic curve, a divisor is a formal sum of points
with degree
The support of a divisor is the set of points with non-zero coefficients in the sum.
The divisor of a function f, denoted or , is supported on the poles and zeroes of the function, with coefficients the degree of the pole or zero, with positive sign for zeroes and negative sign for poles. The degree of the divisor of a function is zero.