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

摘要

We enumerate, via floor diagrams, complex and real curves in CP2 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. (C) 2015 Elsevier Inc. All rights reserved.