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