On Welschinger invariants of symplectic 4-manifolds

Abstract

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 [BP13].

arXiv comment26 pages, 9 figures. v3: many details added, previous sections 2 and 3 have been merged