Outdated Archival Version

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Real enumerative geometry and effective algebraic equivalence

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 be real. Our particular focus is how to use the knowledge that one problem can have all its solutions be real to deduce that other, related problems do as well. The primary technique is to deform intersections of subvarieties into simple cycles. These methods also give lower bounds on the number of real solutions that are possible for a particular enumerative problem.