Floor diagrams relative to a conic, and GW-W invariants of Del Pezzo surfaces

Abstract

We enumerate, via floor diagrams, complex and real curves in the projective plane blown up in $n$ points on a conic. As an application, we deduce Gromov-Witten and Welschinger invariants of Del Pezzo surfaces. These results are mainly obtained using Li's degeneration formula and its real counterpart.

arXiv comment49 pages, 8 figures, v3: correction of a small mistake in the computations of example 7.9 (that unfortunately remains present in the published version)