Behavior of Welschinger Invariants under Morse Simplifications

Details Behavior of Welschinger Invariants under Morse Simplifications Behavior of Welschinger Invariants under Morse Simplifications

2012-03-13

arxiv.org/abs/1203.2773v1

Mathematics

Algebraic Geometry

6 pages. This text is an announcement, it does not contain proofs

Scientific paper

We relate Welschinger invariants of a real Del Pezzo surface of degree at least 3 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 two real versions of a formula by Abramovich, Bertram and Vakil, which computes Gromov-Witten invariants of a weak Del Pezzo surface by means of enumeration of curves. In addition, we give some qualitative consequences of our study, for example decrease of Welschinger invariants relatively to the Euler characteristic of the real part of the surface.

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