RATIONAL CUSPIDAL CURVES ON DEL-PEZZO SURFACES

Abstract

We obtain an explicit formula for the number of rational cuspidal curves of a given degree on a del-Pezzo surface that pass through an appropriate number of generic points of the surface. This enumerative problem is expressed as an Euler class computation on the moduli space of curves. A topological method is employed in computing the degenerate contribution to the Euler class.