TITLE: Is anything known about the enumeration of degree d, genus g curves in CP^2 where g >1 ?
QUESTION [5 upvotes]: I wanted to know if there is something analogous to Kontsevich's recursion formula for 
enumeration of genus zero curves in $\mathbb{C}\mathbb{P}^2$, for higher genus curves. 
There is a 
similar formula for genus one curves. See the book "Mirror Symmetry and Algebraic Geometry"
by Katz, Page 211.
Any partial results known for g>1? That is, maybe its not known for all d, but for some small values of d?

REPLY [9 votes]: The formula is due to Caporaso and Harris, Counting plane curves of any genus, Invent. Math. 131 (1998), no. 2, 345-392, http://arxiv.org/abs/alg-geom/9608025