2012/03/13 by Erwan Brugallé, Brugallé, Erwan, Nicolas Puignau +1 · 1 citation
Mathematics · #14N10 Secondary 14N35 #14P25 #14P99 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 53D45 #math.AG #msc:14N10 #msc:14N35 #msc:14P25 #msc:14P99 #msc:53D45
paper · pdf · doi:10.48550/arxiv.1203.2773
5 pages. This text is an extension of the previous version to symplectic setting. It is an announcement and does not contain proofs
arxiv created 2012/07/11 · arxiv updated 2012/07/12
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 J-holomorphic curves with a non-generic almost complex structure J. In addition, we give some qualitative consequences of our study, for example the vanishing of Welschinger invariants in some cases.