Behavior of Welschinger Invariants Under Morse Simplifications | Zendy

Erwan Brugallé | Zendy; Nicolas Puignau | Zendy

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Behavior of Welschinger Invariants Under Morse Simplifications

Author(s) -

Erwan Brugallé,

Nicolas Puignau

Publication year - 2013

Publication title -

rendiconti del seminario matematico della università di padova

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.329

H-Index - 24

eISSN - 0373-319X

pISSN - 0041-8994

DOI - 10.4171/rsmup/130-4

Subject(s) - morse code , mathematics , computer science , statistical physics , mathematical economics , physics , telecommunications

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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