Geodesic
Surgery of real symplectic fourfolds and Welschinger invariants
Journal of Singularities, Tome 17 (2018), pp. 267-294

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A surgery of a real symplectic manifold X_R along a real Lagrangian sphere S is a modification of the symplectic and real structure on X_R in a neighborhood of S. Genus 0 Welschinger invariants of two real symplectic 4-manifolds differing by such a surgery have been related. In the present paper, we explore some particular situations where general formulas greatly simplify. As an application, we reduce the computation of genus 0 Welschinger invariants of all del Pezzo surfaces to the cases covered in earlier works, and of all R-minimal real conic bundles to the cases covered by others. As a by-product, we establish the existence of some new relative Welschinger invariants. We also generalize earlier results to the enumeration of curves of higher genus, and give relations between hypothetical invariants defined in the same vein as previous works.
DOI : 10.5427/jsing.2018.17l
Classification : 14P05, 14N10, 14N35, 14P25 
@article{10_5427_jsing_2018_17l,
     author = {Erwan Brugall\'e},
     title = {Surgery of real symplectic fourfolds and {Welschinger} invariants},
     journal = {Journal of Singularities},
     pages = {267--294},
     publisher = {mathdoc},
     volume = {17},
     year = {2018},
     doi = {10.5427/jsing.2018.17l},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2018.17l/}
}
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Erwan Brugallé. Surgery of real symplectic fourfolds and Welschinger invariants. Journal of Singularities, Tome 17 (2018), pp. 267-294. doi: 10.5427/jsing.2018.17l

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