Behavior of Welschinger Invariants Under Morse Simplifications

  • Erwan Brugallé

    Ecole Polytechnique, Palaiseau, France
  • Nicolas Puignau

    Universidade Federal do Rio de Janeiro, Brazil


We relate Welschinger invariants of a rational real symplectic 4-manifold before and after a Morse simplification (i.e deletion of a sphere or a handle of the real part of the surface). This relation is a consequence of a real version of Abramovich-Bertram formula which computes Gromov-Witten invariants by means of enumeration of -holomorphic curves with a nongeneric almost complex structure . In addition, we give some qualitative consequences of our study, for example the vanishing of Welschinger invariants in some cases.

Cite this article

Erwan Brugallé, Nicolas Puignau, Behavior of Welschinger Invariants Under Morse Simplifications. Rend. Sem. Mat. Univ. Padova 130 (2013), pp. 147–153

DOI 10.4171/RSMUP/130-4