Floor diagrams relative to a conic, and GW-W invariants of Del Pezzo   surfaces
  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. 
Erwan Brugalle
math.AG math.SG