Rendiconti del Seminario Matematico della Università di Padova

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Volume 130, 2013, pp. 147–153
DOI: 10.4171/RSMUP/130-4

Behavior of Welschinger Invariants Under Morse Simplifications

Erwan Brugallé[1] and Nicolas Puignau[2]

(1) Centre Mathématiques Laurent Schwartz, Ecole Polytechnique, 91128, Palaiseau CEDEX, France
(2) Instituto de Matemática, Universidade Federal do Rio de Janeiro, Cidade Universitária - Ilha do Fundão, RJ 21941-909, Rio de Janeiro, Brazil

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 nongeneric almost complex structure $J$. In addition, we give some qualitative consequences of our study, for example the vanishing of Welschinger invariants in some cases.

Keywords: Real enumerative geometry, Welschinger invariants, Gromov-Witten invariants, symplectic sum formula

Brugallé Erwan, Puignau Nicolas: Behavior of Welschinger Invariants Under Morse Simplifications. Rend. Sem. Mat. Univ. Padova 130 (2013), 147-153. doi: 10.4171/RSMUP/130-4