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Principal divisor on an algebraic curve ( $(f)$ )

For a nonzero rational function

f

on a smooth projective curve

C

, its principal divisor is

(f) = div (f) = \sum_{p \in C} ord_{p} (f) p .

It records the zeros of

f

with positive multiplicity and its poles with negative multiplicity. Every principal divisor has degree zero.

Table of contents 130 2
- Divisor class on the projective line Principal divisor on an algebraic curve 50
- Principal divisor with one simple zero and one simple pole Principal divisor on an algebraic curve 45

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