English

Behavior of Welschinger Invariants under Morse Simplifications

Algebraic Geometry 2012-07-12 v2

Abstract

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 JJ-holomorphic curves with a non-generic almost complex structure JJ. In addition, we give some qualitative consequences of our study, for example the vanishing of Welschinger invariants in some cases.

Keywords

Cite

@article{arxiv.1203.2773,
  title  = {Behavior of Welschinger Invariants under Morse Simplifications},
  author = {Erwan Brugallé and Nicolas Puignau},
  journal= {arXiv preprint arXiv:1203.2773},
  year   = {2012}
}

Comments

5 pages. This text is an extension of the previous version to symplectic setting. It is an announcement and does not contain proofs

R2 v1 2026-06-21T20:33:13.723Z