Thursday, 23 September 2010

ag.algebraic geometry - Is anything known about the enumeration of degree d, genus g curves in CP^2 where g >1 ?

There is a combinatorial formula for the number of geometric genus g curves of degree d (possibly reducible) passing through 3d1+g generic points of mathbbP2 (or a more general toric surface) derived by tropical techniques, see



Grigory Mikhalkin, Enumerative tropical algebraic geometry in mathbbR2,
J. Amer. Math. Soc. 18 (2005), no. 2, 313–377 MR

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