Real GromovWitten Theory in All Genera and Real Enumerative Geometry: Computation
Abstract
The first part of this work constructs real positivegenus GromovWitten invariants of realorientable symplectic manifolds of odd "complex" dimensions; the second part studies the orientations on the moduli spaces of real maps used in constructing these invariants. The present paper applies the results of the latter to obtain quantitative and qualitative conclusions about the invariants defined in the former. After describing large collections of realorientable symplectic manifolds, we show that the real genus 1 GromovWitten invariants of sufficiently positive almost Kahler threefolds are signed counts of real genus 1 curves only and thus provide direct lower bounds for the counts of these curves in such targets. We specify real orientations on the realorientable complete intersections in projective spaces; the real GromovWitten invariants they determine are in a sense canonically determined by the complete intersection itself, (at least) in most cases. We also obtain equivariant localization data that computes the real invariants of projective spaces and determines the contributions from many torus fixed loci for other complete intersections. Our results confirm Walcher's predictions for the vanishing of these invariants in certain cases and for the localization data in other cases.
 Publication:

arXiv eprints
 Pub Date:
 October 2015
 arXiv:
 arXiv:1510.07568
 Bibcode:
 2015arXiv151007568G
 Keywords:

 Mathematics  Algebraic Geometry;
 High Energy Physics  Theory;
 Mathematics  Symplectic Geometry;
 14N35;
 53D45
 EPrint:
 66 pages, 3 figures