Commentarii Mathematici Helvetici


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Volume 90, Issue 4, 2015, pp. 905–938
DOI: 10.4171/CMH/373

Published online: 2015-12-03

On Welschinger invariants of symplectic 4-manifolds

Erwan Brugallé[1] and Nicolas Puignau[2]

(1) Ecole Polytechnique, Palaiseau, France
(2) Universidade Federal do Rio de Janeiro, Brazil

We prove the vanishing of many Welschinger invariants of real symplectic 4-manifolds. In some particular instances, we also determine their sign and show that they are divisible by a large power of 2. Those results are a consequence of several relations among Welschinger invariants obtained by a real version of symplectic sum formula. In particular, this note contains proofs of results announced in [4].

Keywords: Real enumerative geometry, Welschinger invariants, Gromov–Witten invariants, symplectic sum formula, symplectic field theory

Brugallé Erwan, Puignau Nicolas: On Welschinger invariants of symplectic 4-manifolds. Comment. Math. Helv. 90 (2015), 905-938. doi: 10.4171/CMH/373