Rational functions with real critical points and the B. and M. Shapiro conjecture in real enumerative geometry
| dc.creator | Eremenko, A. | |
| dc.creator | Gabrielov, A. | |
| dc.date | 2004-05-11 | |
| dc.date.accessioned | 2026-07-07T05:08:08Z | |
| dc.date.available | 2026-07-07T05:08:08Z | |
| dc.description | Suppose that 2d-2 tangent lines to the rational normal curve z\mapsto (1 : z : ... : z^d) in d-dimensional complex projective space are given. It was known that the number of codimension 2 subspaces intersecting all these lines is always finite; for a generic configuration it is equal to the d^{th} Catalan number. We prove that for real tangent lines, all these codimension 2 subspaces are also real, thus confirming a special case of a general conjecture of B. and M. Shapiro. This is equivalent to the following result: If all critical points of a rational function lie on a circle in the Riemann sphere (for example on the real line), then the function maps this circle into a circle. | |
| dc.description | 25 pages, published version | |
| dc.identifier | https://arxiv.org/abs/math/0405196 | |
| dc.identifier | http://arxiv.org/abs/math/0405196 | |
| dc.identifier | Ann. of Math. (2) 155 (2002), no. 1, 105--129 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71139 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.title | Rational functions with real critical points and the B. and M. Shapiro conjecture in real enumerative geometry | |
| dc.type | text |