REAL ENUMERATIVE GEOMETRY AND EFFECTIVE ALGEBRAIC EQUIVALENCE

We study when a problem in enumerative geometry may have all of its so lutions be real and show that many Schubert-type enumerative problems on some flag manifolds can have all of their solutions real. Our parti cular focus is to find how to use the knowledge that one problem can h ave all its solutions to be real to deduce that other, related problem s do as well. The primary technique is to study deformations of inters ections of subvarieties into simple cycles. These methods may also be used to give lower bounds on the number of real solutions that are pos sible for a given enumerative problem. (C) 1997 Elsevier Science B.V.