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Izv. RAN. Ser. Mat., 2019, Volume 83, Issue 4, Pages 129–157 (Mi izv8797)  

On the variety of the inflection points of plane cubic curves

Vik. S. Kulikov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: In this paper we study properties of the nine-dimensional variety of the inflection points of plane cubics. We describe the local monodromy groups of the set of inflection points near singular cubic curves and give a detailed description of the normalizations of the surfaces of the inflection points of plane cubic curves belonging to general two-dimensional linear systems of cubics. We also prove the vanishing of the irregularity of a smooth manifold birationally isomorphic to the variety of the inflection points of plane cubics.

Keywords: plane cubic curves, inflection points, monodromy.

DOI: https://doi.org/10.4213/im8797

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English version:
Izvestiya: Mathematics, 2019, 83:4, 770–795

Bibliographic databases:

UDC: 512.774.4
MSC: Primary 14H50; Secondary 14H52
Received: 13.04.2018
Revised: 09.08.2018

Citation: Vik. S. Kulikov, “On the variety of the inflection points of plane cubic curves”, Izv. RAN. Ser. Mat., 83:4 (2019), 129–157; Izv. Math., 83:4 (2019), 770–795

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  • http://mi.mathnet.ru/eng/izv8797
  • https://doi.org/10.4213/im8797
  • http://mi.mathnet.ru/eng/izv/v83/i4/p129

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