Mathematics – Algebraic Geometry
Scientific paper
2001-02-09
Math. Scand. 92 (2003), 223-245.
Mathematics
Algebraic Geometry
19 pages, LaTeX, uses rsfs fonts. Tables and maple code hidden in source
Scientific paper
This note pursues the techniques of modified psi classes on the stack of stable maps (cf. [Graber-Kock-Pandharipande]) to give concise solutions to the characteristic number problem of rational curves in P^2 or P^1 x P^1 with a cusp or a prescribed triple contact. The classes of such loci are computed in terms of modified psi classes, diagonal classes, and certain codimension-2 boundary classes. Via topological recursions the generating functions for the numbers can then be expressed in terms of the usual characteristic number potentials.
Kock Joachim
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