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arXiv · 1203.2773

Behavior of Welschinger Invariants under Morse Simplifications

Erwan Brugallé·Nicolas Puignau
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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 $J$-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.

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Erwan Brugallé, Nicolas Puignau. 2012-03-13. Behavior of Welschinger Invariants under Morse Simplifications. https://arxiv.org/abs/1203.2773

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