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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2017: 1.49

Online
ISSN
1435-5345
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Volume 2016, Issue 714

A congruence modulo four in real Schubert calculus

Nickolas Hein
/ Frank Sottile
/ Igor Zelenko
Published Online: 2014-02-12 | DOI: https://doi.org/10.1515/crelle-2013-0122

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.

Revised: 2013-10-22

Published Online: 2014-02-12

Published in Print: 2016-05-01

Funding Source: NSF

Award identifier / Grant number: DMS-1001615

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2016, Issue 714, Pages 151–174, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102,

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