Pencils of cubics as tools to solve an interpolation problem

Touzé, Séverine Fiedler-Le

doi:10.1007/s00200-006-0028-3

Cited by 3 publications

(3 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We indicated how this description can be derived from our results using Cremona transformations. We sketched also an application: a method (alternative to that of [4]) to describe the topology of real rational cubics passing through the points of a 7-configuration.…”

Section: 21mentioning

confidence: 99%

See 2 more Smart Citations

Deformation classification of typical configurations of 7 points in the real projective plane

Finashin

Zabun

2015

Topology and its Applications

View full text Add to dashboard Cite

A configuration of 7 points in RP 2 is called typical if it has no collinear triples and no coconic sextuples of points. We show that there exist 14 deformation classes of such configurations. This yields classification of real Aronhold sets."This is one of the ways in which the magical number seven has persecuted me."George A. Miller, The magical number seven, plus or minus two: some limits of our capacity for processing information 2010 Mathematics Subject Classification. Primary:14P25. Secondary: 14N20.

show abstract

Section: 21mentioning

confidence: 99%

“…Acknowledgments. This paper is essentially based on [13], which was partially motivated by our attempts to understand and develop the results of [4].…”

Section: 21mentioning

confidence: 99%

See 1 more Smart Citation

Deformation classification of typical configurations of 7 points in the real projective plane

Finashin

Zabun

2015

Topology and its Applications

View full text Add to dashboard Cite

show abstract

Frontiers of reality in Schubert calculus

Sottile

2009

Bull. Amer. Math. Soc.

View full text Add to dashboard Cite

Abstract. The theorem of Mukhin, Tarasov, and Varchenko (formerly the Shapiro conjecture for Grassmannians) asserts that all (a priori complex) solutions to certain geometric problems in the Schubert calculus are actually real. Their proof is quite remarkable, using ideas from integrable systems, Fuchsian differential equations, and representation theory. There is now a second proof of this result, and it has ramifications in other areas of mathematics, from curves to control theory to combinatorics. Despite this work, the original Shapiro conjecture is not yet settled. While it is false as stated, it has several interesting and not quite understood modifications and generalizations that are likely true, and the strongest and most subtle version of the Shapiro conjecture for Grassmannians remains open.

show abstract

M ‐curves of degree 9 with deep nests

Touzé

2009

Journal of the London Mathematical Society

View full text Add to dashboard Cite

The first part of Hilbert's sixteenth problem deals with the classification of the isotopy types realizable by real plane algebraic curves of given degree m. For m ≥ 8, one restricts the study to the case of the M -curves. For m = 9, the classification is still wide open. We say that an M -curve of degree 9 has a deep nest if it has a nest of depth 3. In the present paper, we prohibit 10 isotopy types with deep nest and no outer ovals.

show abstract

Pencils of cubics as tools to solve an interpolation problem

Cited by 3 publications

References 4 publications

Deformation classification of typical configurations of 7 points in the real projective plane

Deformation classification of typical configurations of 7 points in the real projective plane

Frontiers of reality in Schubert calculus

M ‐curves of degree 9 with deep nests

Contact Info

Product

Resources

About