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arXiv · 1309.4079

Enumeration of real curves in CP^{2n-1} and a WDVV relation for real Gromov-Witten invariants

Penka Georgieva·Aleksey Zinger
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Abstract

We establish a homology relation for the Deligne-Mumford moduli spaces of real curves which lifts to a WDVV-type relation for real Gromov-Witten invariants of real symplectic manifolds; we also obtain a vanishing theorem for these invariants. For many real symplectic manifolds, these results reduce all genus 0 real invariants with conjugate pairs of constraints to genus 0 invariants with a single conjugate pair of constraints. In particular, we give a complete recursion for counts of real rational curves in odd-dimensional projective spaces with conjugate pairs of constraints and specify all cases when they are nonzero and thus provide non-trivial lower bounds in high-dimensional real algebraic geometry. We also show that the real invariants of the three-dimensional projective space with conjugate point constraints are congruent to their complex analogues modulo 4.

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Penka Georgieva, Aleksey Zinger. 2013-09-16. Enumeration of real curves in CP^{2n-1} and a WDVV relation for real Gromov-Witten invariants. https://doi.org/10.1215/00127094-2017-0023

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