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Izvestiya: Mathematics, 2013, Volume 77, Issue 4, Pages 675–695
DOI: https://doi.org/10.1070/IM2013v077n04ABEH002655 (Mi im8015) 		 
Combinatorics associated with inflections and bitangents of plane quartics

M. Kh. Gizatullin

Togliatti State University
English version PDF (340 kB) Russian version article
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DOI: https://doi.org/10.1070/IM2013v077n04ABEH002655
Abstract: After a preliminary survey and a description of some small Steiner systems from the standpoint of the theory of invariants of binary forms, we construct a binary Golay code (of length 24) using ideas from J. Grassmann's thesis of 1875. One of our tools is a pair of disjoint Fano planes. Another application of such pairs and properties of plane quartics is a construction of a new block design on 28 objects. This block design is a part of a dissection of the set of 288 Aronhold sevens. The dissection distributes the Aronhold sevens into 8 disjoint block designs of this type.
Keywords: binary form, invariant, point of inflection, bitangent, plane quartic, Aronhold seven, block design, Fano plane, Steiner system, Golay code.
Received: 25.06.2012
Revised: 14.11.2012
Bibliographic databases:
Document Type: Article
UDC: 512.772+519.725+519.172
MSC: 14H50, 05B05, 94B25
Language: English
Original paper language: Russian
Citation: M. Kh. Gizatullin, “Combinatorics associated with inflections and bitangents of plane quartics”, Izv. Math., 77:4 (2013), 675–695
Citation in format AMSBIB
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\paper Combinatorics associated with inflections and bitangents of plane quartics
\jour Izv. Math.
\yr 2013
\vol 77
\issue 4
\pages 675--695
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  • https://www.mathnet.ru/eng/im/v77/i4/p31
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Russian version PDF:240
    English version PDF:16
    References:47
    First page:19
     
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