Classification of nonsingular surfaces of degree 4 in \({\mathbb{R}}{\mathbb{P}}^ 3\) with respect to rigid isotopies
type: Item
instance of: scholarly article
title: Classification of nonsingular surfaces of degree 4 in \({\mathbb{R}}{\mathbb{P}}^ 3\) with respect to rigid isotopies
zbMATH Open document ID: 0577.14014
DOI: 10.1007/BF01076360
publication date: 1984-01-01T00:00:00Z
review text: This paper studies the classification of the non-singular surfaces of degree 4 in \(RP^ 3\). This problem was initiated by \textit{D. Hilbert} [Nachr. Kgl. Ges. Wiss. Göttingen, Math.-Phys. Kl. 1909, 308-313 (1909)] and \textit{K. Rohn} [Ber. Verhdl. Kgl. Sächs. Ges. Wiss. Leipzig 63, 423-440 (1911) and Math. Ann. 73, 177-229 (1913)]. The author considers a new method for the proposed classification with respect to rigid isotopies. The method used is based on the Torelli theorem for algebraic surfaces of type K 3 and a result of \textit{V. S. Kulikov} [Usp. Mat. Nauk 32, No.4(196), 257-258 (1977; Zbl 0449.14008)]. The author defines the homological type of a surface by a 4-uple (E,B,h,t). The paper contains a detailed study of the homological type. It is established that to every class of projectively equivalent surfaces there are at most two classes with respect to rigid equivalence. The isotopic classification consists of 113 classes. The author remarks that a recent result of \textit{O. Ya. Viro} establishes that the rigid isotopic classification consists of 169 classes.
Mathematics Subject Classification ID: 14F35
Mathematics Subject Classification ID: 14F45
Mathematics Subject Classification ID: 14J10
zbMATH DE Number: 3922837
zbMATH Keywords: classification of the non-singular surfaces of degree 4
zbMATH Keywords: Torelli theorem
zbMATH Keywords: homological type
zbMATH Keywords: isotopic classification
author: Viatcheslav Kharlamov
MaRDI profile type: Publication
cites work: Q3877793
cites work: THE TOPOLOGY OF REAL PROJECTIVE ALGEBRAIC VARIETIES
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published in: Functional Analysis and Its Applications
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description: scientific article; zbMATH DE number 3922837