Real enumerative geometry and effective algebraic equivalence Original Research Article

We study when a problem in enumerative geometry may have all of its solutions be real and show that many Schubert-type enumerative problems on some flag manifolds can have all of their solutions real. Our particular focus is to find how to use the knowledge that one problem can have all its solutions to be real to deduce that other, related problems do as well. The primary technique is to study deformations of intersections of subvarieties into simple cycles. These methods may also be used to give lower bounds on the number of real solutions that are possible for a given enumerative problem.