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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

12 Issues per year


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A congruence modulo four in real Schubert calculus

1Department of Mathematics, University of Nebraska at Kearney, Kearney, NE 68849, USA

2Department of Mathematics, Texas A&M University, College Station, TX 77843, USA

3Department of Mathematics, Texas A&M University, College Station, TX 77843, USA

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crelle-2013-0122, February 2014

Publication History

Received:
2012-12-03
Revised:
2013-10-22
Published Online:
2014-02-12

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.

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