منابع مشابه
Lower bounds in real Schubert calculus
We describe a large-scale computational experiment studying structure in the numbers of real solutions to osculating instances of Schubert problems. This investigation uncovered Schubert problems whose computed numbers of real solutions variously exhibit nontrivial upper bounds, lower bounds, gaps, and a congruence modulo four. We present a family of Schubert problems, one in each Grassmannian,...
متن کاملDegree Bounds in Quantum Schubert Calculus
Fulton and Woodward [8] have recently identified the smallest degree of q that appears in the expansion of the product of two Schubert classes in the (small) quantum cohomology ring of a Grassmannian. We present a combinatorial proof of this result, and provide an alternative characterization of this smallest degree in terms of the rim hook formula [2] for the quantum product.
متن کاملThe Special Schubert Calculus Is Real
We show that the Schubert calculus of enumerative geometry is real, for special Schubert conditions. That is, for any such enumerative problem, there exist real conditions for which all the a priori complex solutions are real. Fulton asked how many solutions to a problem of enumerative geometry can be real, when that problem is one of counting geometric figures of some kind having specified pos...
متن کاملRational Functions and Real Schubert Calculus
We single out some problems of Schubert calculus of subspaces of codimension 2 that have the property that all their solutions are real whenever the data are real. Our arguments explore the connection between subspaces of codimension 2 and rational functions of one variable.
متن کاملThe Secant Conjecture in the Real Schubert Calculus
We formulate the Secant Conjecture, which is a generalization of the Shapiro Conjecture for Grassmannians. It asserts that an intersection of Schubert varieties in a Grassmannian is transverse with all points real if the flags defining the Schubert varieties are secant along disjoint intervals of a rational normal curve. We present theoretical evidence for this conjecture as well as computation...
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ژورنال
عنوان ژورنال: The São Paulo Journal of Mathematical Sciences
سال: 2013
ISSN: 2316-9028,1982-6907
DOI: 10.11606/issn.2316-9028.v7i1p33-58