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Amoebas of Cuspidal Strata for Classical Discriminant

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Complex Analysis and Geometry

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 144))

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Abstract

An amoeba of an analytic set is the real part of its image in a logarithmic scale. Among all hypersurfaces A-discriminantal sets have the most simple amoebas. We prove that any singular cuspidal stratum of the classical discriminant can be transformed by a monomial change of variables into an A-discriminantal set and compute the contours of the amoebas of these strata.

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Acknowledgments

The first author is supported by the RFBR, research project no. 14-01-31265 mol_a. The second author is supported by the RFBR, research project no. 14-01-31239 mol_a. The third author is supported by the RFBR, research project no. 14-01-00544_a.

The research for this paper was carried out in Siberian Federal University within the framework of the research project ‘Multidimensional Complex Analysis and Differential Equations’ funded by the grant of the Russian Federation Government to support scientific research under the supervision of leading scientist, no. 14.Y26.31.0006.

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Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Siberian Federal University, pr. Svobodny 79, 660041, Krasnoyarsk, Russia

    E. N. Mikhalkin, A. V. Shchuplev & A. K. Tsikh

Authors
  1. E. N. Mikhalkin
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  2. A. V. Shchuplev
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  3. A. K. Tsikh
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Corresponding author

Correspondence to A. K. Tsikh .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Università di Roma Tor Vergata, Rome, Italy

    Filippo Bracci

  2. Dept. of Mathematics Education, Kyungnam University, Changwon, Korea (Republic of)

    Jisoo Byun

  3. Université Joseph Fourier Grenoble, Institut Fourier, Grenoble, France

    Hervé Gaussier

  4. Graduate School of Mathematical Sciences, The University of Tokyo, Meguro-ku, Tokyo, Japan

    Kengo Hirachi

  5. Department of Mathematics, POSTECH, Pohang, Korea (Republic of)

    Kang-Tae Kim

  6. Department of Mathematics, Bergische Universität Wuppertal, Wuppertal, Nordrhein-Westfalen, Germany

    Nikolay Shcherbina

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Mikhalkin, E.N., Shchuplev, A.V., Tsikh, A.K. (2015). Amoebas of Cuspidal Strata for Classical Discriminant. In: Bracci, F., Byun, J., Gaussier, H., Hirachi, K., Kim, KT., Shcherbina, N. (eds) Complex Analysis and Geometry. Springer Proceedings in Mathematics & Statistics, vol 144. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55744-9_19

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