A congruence modulo four in real Schubert calculus

Nickolas Hein; Frank Sottile; Igor Zelenko

doi:10.1515/crelle-2013-0122

Article

A congruence modulo four in real Schubert calculus

Nickolas Hein , Frank Sottile and Igor Zelenko

Published/Copyright: February 12, 2014

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From the journal Journal für die reine und angewandte Mathematik (Crelles Journal) Volume 2016 Issue 714

Abstract

We establish a congruence modulo four in the real Schubert calculus on the Grassmannian of m-planes in 2m-space. This congruence holds for fibers of the Wronski map and a generalization to what we call symmetric Schubert problems. This strengthens the usual congruence modulo two for numbers of real solutions to geometric problems. It also gives examples of geometric problems given by fibers of a map whose topological degree is zero but where each fiber contains real points.

Funding source: NSF

Award Identifier / Grant number: DMS-1001615

Funding statement:

Received: 2012-12-3

Revised: 2013-10-22

Published Online: 2014-2-12

Published in Print: 2016-5-1

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Articles in the same Issue

https://doi.org/10.1515/crelle-2013-0122