Real Gromov-Witten theory in all genera and real enumerative geometry: computation

摘要: Gromov–Witten invariants of real-orientable symplectic manifolds odd “complex” dimensions; the second part studies orientations on moduli spaces real maps used in constructing these invariants. The present paper applies results latter to obtain quantitative and qualitative conclusions about defined former. After describing large collections manifolds, we show that genus $1$ sufficiently positive almost Kahler threefolds are signed counts 1 curves only and, thus, provide direct lower bounds for such targets. We specify complete intersections projective spaces; they determine a sense canonically determined by intersection itself, (at least) most cases. also equivariant localization data computes determines contributions from many torus fixed loci other intersections. Our confirm Walcher’s predictions vanishing certain cases is demonstrate non-triviality our higher genera separate paper.