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Perspectives in Analysis, Geometry, and Topology pp 67–79Cite as

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Toward a Generalized Shapiro and Shapiro Conjecture

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Part of the book series: Progress in Mathematics ((PM,volume 296))

Abstract

We obtain a new, asymptotically better, bound \(g \leq \frac{1} {4}{d}^{2} + O(d)\) on the genus of a curve that may violate the generalized total reality conjecture. The bound covers all known cases except g = 0 (the original conjecture).

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References

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Acknowledgements

I am grateful to T. Ekedahl and B. Shapiro for the fruitful discussions of the subject. This work was completed during my participation in the special semester on Real and Tropical Algebraic Geometry held at Centre Interfacultaire Bernoulli, École polytechnique fédérale de Lausanne. I extend my gratitude to the organizers of the semester and to the administration of CIB.

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Authors and Affiliations

  1. Department of Mathematics, Bilkent University, 06800, Ankara, Turkey

    Alex Degtyarev

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  1. Alex Degtyarev
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Correspondence to Alex Degtyarev .

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Editors and Affiliations

  1. Université Pierre et Marie Curie and Institut Universitaire de France Institut de Mathématiques de Jussieu, 4 place Jussieu, 75005, Paris, France

    Ilia Itenberg

  2. Institut des Hautes Études Scientifiques Le Bois-Marie, 35, route de Chartres, Bures-sur-Yvette, 91440, France

    Burglind Jöricke

  3. Department of Mathematics, Stockholm University, Stockholm, SE-10691, Sweden

    Mikael Passare

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Degtyarev, A. (2012). Toward a Generalized Shapiro and Shapiro Conjecture. In: Itenberg, I., Jöricke, B., Passare, M. (eds) Perspectives in Analysis, Geometry, and Topology. Progress in Mathematics, vol 296. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8277-4_4

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