Let \(C\subset\CP^2\) be the zero locus of a homogeneous polynomial of degree \(5\) and assume that \(C\) is smooth. Let \(D\) be a divisor on \(C\) of degree \(11\). What is the most you can say about \[ \dim\Gamma(D)? \] For example: is it positive; can you give a lower bound; can you give an upper bound; or can you determine it exactly? Justify your answer.
Dimension bounds for $\Gamma(D)$ on a smooth plane quintic
P-UNL970953-04-AG3
- Area
- Algebraic Geometry
- Seen at
- UNL
- Years
- 2004
- Status
- draft