Maximally inflected real rational curves

Details Maximally inflected real rational curves Maximally inflected real rational curves

2002-06-25

arxiv.org/abs/math/0206268v2

Moscow Mathematics Journal 3 (2003), no. 3, 947--987, 1199--1200.

Mathematics

Algebraic Geometry

Revised with minor corrections. 37 pages with 106 .eps figures. Over 250 additional pictures on accompanying web page (See h

Scientific paper

We introduce and begin the topological study of real rational plane curves, all of whose inflection points are real. The existence of such curves is a corollary of results in the real Schubert calculus, and their study has consequences for the important Shapiro and Shapiro conjecture in the real Schubert calculus. We establish restrictions on the number of real nodes of such curves and construct curves realizing the extreme numbers of real nodes. These constructions imply the existence of real solutions to some problems in the Schubert calculus. We conclude with a discussion of maximally inflected curves of low degree.

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