The Di Francesco-Itzykson-Göttsche Conjectures for Node Polynomials of
arXiv:1010.2377 · doi:10.1142/S0129167X12500498
Abstract
For a smooth, irreducible projective surface S over \mathbb{C}, the number of r-nodal curves in an ample linear system |L| (where L is a line bundle on S) can be expressed using the rth Bell polynomial P_{r} in r universal functions a_{i} of (S,L), which are linear polynomials in the four Chern numbers of S and L. We use this result to establish a proof of the classical shape conjectures of Di Francesco-Itzykson and Göttsche governing node polynomials in the case of P^{2}. We also give a recursive procedure which provides the L^{2}-term of the polynomials a_{i}.
17 pages: Updated version of published paper, with a correction in Lemma 2.1. 1 page: Attached correction sheet, displaying changes made to published version; Int. J. Math., Vol. 23, No. 4, 2012