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THE DI FRANCESCO–ITZYKSON–GÖTTSCHE CONJECTURES FOR NODE POLYNOMIALS OF ℙ²

NIKOLAY QVILLER

Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053 Blindern, NO-0316 Oslo, Norway

https://doi.org/10.1142/S0129167X12500498Cited by:5 (Source: Crossref)

Abstract

For a smooth, irreducible projective surface S over ℂ, the number of r-nodal curves in an ample linear system (where is a line bundle on S) can be expressed using the rth Bell polynomial P_r in universal functions a_i, 1 ≤ i ≤ r, of (S, ), which are ℤ-linear polynomials in the four Chern numbers of S and . 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 ℙ². We also give a recursive procedure which provides the -term of the polynomials a_i.

Keywords:

AMSC: 14N10, 14H50, 14Q05, 05A10

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